THE OF EQUITY DERIVATIVES AND STRUCTURED PRODUCTS

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ALTIPLANO An Altiplano is a type of mountain range A structure, which offers investors a fixed payout at the end of the product’s life on the condition that none of the assets that make up the underlying basket have decreased A CCRETING below a given level. If the level is breached, A description, applicable to a variety of the product pays a capital guarantee plus instruments, denoting that the notional participation in the growth of the total principal increases successively over the underlying basket. life of the instrument, eg, caps, collars, swaps and . If the increase AMERICAN-STYLE takes place in increments, the instrument may be known as a step-up. See also The holder of an American-style option has amortising the right to the option at any time during he life of the option, up to and including the expiry date. See also option A CCRUAL CORRIDOR styles The range within which an underlying reference rate must trade for AMORTISING payments to accrue in a range note or corridor option. A description, applicable to a variety of instruments, denoting that the notional principal decreases successively over the life A CCRUAL NOTE of an instrument, eg, amortising , index See range note amortising rate swap, amortising cap, amortising , amortising . If the ACCRUAL PERIOD decrease takes place in increments, the instrument may be known as a step-down. Period over which net payment or receipt Mortgage-style amortisation refers to an pertaining to swaps is accrued. It is such that the principal inclusive of the start date and runs to the amortisation plus is the same amount end date without including the end date. in each interest period. See also accreting ALL-OR-NOTHING OPTION See ANNAPURNA An Annapurna is a kind of mountain range product, which offers a return equal to the Alpha is used to measure the performance greater of a capital guarantee plus a fixed of a fund in relation to its benchmark. An coupon and a participation in the alpha hat measures 2.0 indicates a fund performance of the underlying basket. The has achieved a return 2% better than level of the fixed coupon and of the could have been expected from its participation rate in the performance depend benchmark. Alternative risk transfer An on if and when the worst-performing approach to risk management combining breaches a downside barrier. The later the capital markets, reinsurance and breach, the higher the fixed coupon and techniques that allows equity participation rate. a party to either free itself from risks not easily transferred via traditional , ANNUITY SWAP or alternatively cover such risks in a non- An swap in which a series of traditional way – by using the capital irregular cashflows are exchanged for a markets for example. stream of regular cashflows of equivalent .

1 Equity Derivatives Glossary

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ASSET/LIABILITY MANAGEMENT The practice of matching the term structure A guaranteed or riskless profit from and cashflows of an organisation’s asset and simultaneously buying and selling liability portfolios in order to maximise returns instruments that are perfect equivalents, and minimise risk. An institutional example of the first being cheaper than the second. this would be a bank converting a fixed-rate

loan (asset) by utilising a fixed-for-floating ARBITRAGE-FREE MODEL to match its floating rate Any model that does not allow arbitrage on funding (deposits). the underlying variable. Some simple early models assumed parallel shifts in the AT-THE-MONEY curve, but the varying yields of different 1.At-the-money forward: An option whose duration bonds could be arbitraged using strike is set at the same level as the strategies. prevailing market price of the underlying

. With a Black-Scholes AUTOREGRESSIVE CONDITIONAL model, the delta of a European-style, at-the- heteroscedasticity (Arch) money forward option will be close to 50%. A discrete time model for a random 2.At-the-money spot: An option whose strike variable. It assumes that is is set the same as the prevailing market price stochastic and is a function of the variance of the underlying. Because forwards of previous time steps and the level of the commonly trade at a premium or discount to underlying. the spot, the delta may not be close to 50%. See also in-the-money, out-of-the-money

ASIAN OPTION AUTOCAP See average option A standard cap consists of a series of caplets hedging future floating rate payments. ASSET ALLOCATION However, autocaps only provide a for The distribution of investment funds within the first pre-specified number of in-the-money a single asset class or across a number of caplets after which the option expires, and so asset classes (such as equities, bonds are a cheaper alternative to caps. and commodities) with the aim of diversifying risk or adding value to a AVERAGE OPTION portfolio. See also overlay A plain vanilla option pays out the difference between its predetermined and ASSET BACKED the spot rate (or price) of the underlying at An asset backed security is a security the time of expiry. The purchaser of an collateralised by assets such as bonds, average option (average price, average repayments, loan repayments strike, average hybrid, average ratio), on the or real estate. other hand, will receive a pay-out which depends on the average value of the underlying. The average can be calculated in a number of ways (arithmetic or geometric, A package of a cash credit instrument and weighted or simple) from the spot rate on a a corresponding swap that transforms the predetermined series of dates. An average cash lows of the non-par instrument ( rate (or average price) option is a cash- or loan), into a par (floating interest rate) settled option with a predetermined (ie fixed) structure. strike which is exercised at expiry against the Asset swaps typically transform fixed-rate average value of the underlying over the bonds into par floaters, bearing a net specified dates. In general, hedging with an coupon of plus a spread, although average option is cheaper than using a cross-currency asset swaps, transforming portfolio of vanilla options, since the cashflows from one currency to another averaging process offsets high values with are also common.

2 Equity Derivatives Glossary

A/B low ones and therefore lowers dependent options which are either activated and premium. (knocked-in) or terminated (knocked-out) if a Average options, also known as Asian specified spot rate reaches a specified trigger options, are particularly popular in the level (or levels) between inception and expiry. equity, currency and commodity markets. Before termination knock-out options behave In contrast, the strike for an average strike identically to standard European-style option is not fixed until the end of the options, but carry lower initial premiums averaging period which is typically much because they may be extinguished before before the expiry. When the strike is set, reaching . In contrast, knock-in the option is exercised against the options behave identically to European-style prevailing spot rate. Unlike average price options only if they are activated/ knocked-in options, average strike options may be and so also command a lower premium. either cash or physically settled. In the The standard barrier options have barrier case of an average hybrid option (also levels that are monitored continually during known as an average-in/average-out the lifetime of the option. Single ), both the strike and settlement options that have a barrier level above price of the option are determined using current spot are classified as up-and-out or the average, where the strike averaging up-and-in options. For single barriers below period typically precedes the settlement spot the usual terminology is down-and-out price averaging period. For the average for the knock-out barrier option, and down- ratio option, both the strike and settlement and-in for the knock-in barrier option. price of the option are determined using Many variations on the barrier theme are the average as in the hybrid case.The final available. Barrier levels can be monitored payout is determined by comparing the continually, at discrete fixing times (discrete ratio of settlement price to strike and a barrier options) or only at the final expiry date fixed percent strike. of the option (at-expiry barrier options). Barriers may be active only during distinct AVERAGE PRICE OPTION time intervals (window barrier options) or may change value at fixed points during the See average option lifetime of the option (stepped barrier options). Barriers may need to be breached AVERAGE RATE OPTION for a certain time before they are considered See average option triggered (Parisian Barrier Options) or may allow for partial triggering depending upon how far beyond the trigger level the AVERAGE STRIKE OPTION underlying asset is observed (Soft Barrier See average option options). Barriers may reference a different underlying to that of the option itself – such barriers are known as outside barriers. See also discrete barrier option, double barrier option, Parisian barrier option, path- B dependent option, trigger, trigger condition

BASIS BACK-TESTING 1.The difference between the price of a The validation of a model by feeding it and its theoretical value. historical data and comparing the model’s 2.The convention for calculating interest results with the historical reality. The rates. A bond can be 30/360 or actual/365 in reliability of this technique generally the US, or 360/360 in Europe. increases with the amount of historical instruments can be actual/360 in the US or data used. actual/365 in the UK and Japan.

BARRIER OPTION BASIS RISK Barrier options, also known as knock-out, In a futures market, the basis risk is the risk knock-in or trigger options, are path- that the value of a futures contract does not

3 Equity Derivatives Glossary

B move in line with the underlying exposure. Types of basket credit default swaps include Because a futures contract is a forward linear basket credit default swaps, first-to- agreement, many factors can affect the default basket credit default swaps, and first- basis. These include shifts in the yield loss basket credit default swaps. See also curve, which affect the cost of carry; a change in the cheapest-to-deliver bond; supply and demand; and changing expectations in the futures market about the market’s direction. Generally, basis An option that enables a purchaser to buy or risk is the risk of a hedge’s price not sell a basket of currencies, equities or bonds. moving in line with the price of the hedged position. For example, hedging swap BASKET SWAP positions with bonds incurs basis risk A swap in which a floating leg is based on the because changes in the swap spread returns on a basket of underlying assets, would result in the hedge being imperfectly such as equities, commodities, bonds, or correlated. Basis risk increases the more swaps. The other leg is usually (but not the instrument to be hedged and the always) a reference interest rate such as underlying are imperfect substitutes. Libor, plus or minus a spread.

BASIS SWAP BASKET TRADING An interest rate or a cross- See currency basis swap is one in which two streams of floating rate payments are exchanged. Examples of interest rate basis swaps include swapping $Libor An option spread trade that reflects a bearish payments for floating , view on the market. It is usually understood Prime, Treasury bills, or Constant Maturity as the purchase of a put spread. See also Treasury rates; this is also known as a , call spread floating-floating swap. A typical cross- currency basis swap exchanges a set of BERMUDAN OPTION Libor payments in one currency for a set of Libor payments in another currency. The holder of a Bermudan option, also known as a mid-Atlantic option, has the right to exercise it on one or more possible dates BASIS TRADING prior to its expiry. See also option styles To basis trade is to deal simultaneously in a contract, normally a future, BEST-OF OPTION and the underlying asset. The purpose of such a trade is either to cover derivatives A best-of option pays out on the best sold, or to attempt an arbitrage strategy. performing of a number of underlying assets This arbitrage can either take advantage over an agreed period of time. of an existing mispricing (in cash-and- For instance, if a basket contains stock A, carry arbitrage) or be based on stock B and stock C and stock B gains in that the basis will change. See value by the larger amount during the also cash-and-carry arbitrage products term, then the payout would be based on the increase in value of Stock B.

BASKET CREDIT DEFAULT SWAP A credit default swap which transfers credit risk with respect to multiple 1. The beta of an instrument is its reference entities. For each reference standardised covariance with its class of entity, an applicable notional amount is instruments as a whole. Thus the beta of a specified, with the notional of the basket stock is the extent to which that stock follows swap equal to the aggregate of the movements in the overall market. specified applicable notional amounts. 2. Beta trading is used by currency traders if they take the volatility risk of one currency in

4 Equity Derivatives Glossary

B another. For example, rather than hedge a BINOMIAL MODEL sterling/yen option with another Any model that incorporates a binomial tree. sterling/yen option, a trader, either because of liquidity constraints or because B of lower volatility, might hedge with INOMIAL TREE euro/yen options. The beta risk indicates Also called a binomial lattice. A discrete time the likelihood of the two currencies’ model for describing the evolution of a volatilities diverging. random variable that is permitted to rise or fall with given probabilities. After the initial BETTER-OF-TWO-ASSETS OPTION rise, two branches will each have two possible outcomes and so the process will See best-of option continue. The process is usually specified so that an upward movement followed by a BILATERAL NETTING downward movement results in the same price, so that the branches recombine. If the Agreement between two counterparties branches do not recombine it is known as a whereby the value of all in-the-money bushy, or exploded, tree. The size of the contracts is offset by the value of all out- movements and the probabilities are chosen of-the money contracts, resulting in a so that the discrete binomial model tends to single net exposure amount owed by one the assumed in option counterparty to the other. Bilateral netting models as the number of discrete steps is can be multi-product and encompass increased. Options can be evaluated by portfolios of swaps, interest rate options, discounting the terminal pay-off back through and forward foreign exchange. the tree using the determined probabilities.

Interest in binomial trees arises from their BINARY OPTION ability to deal with American-style features Unlike simple options, which have and to price interest rate options. For continuous pay-out profiles, that of a example, American-style options can readily binary option is discontinuous and pays be priced because the early exercise out a fixed amount if the underlying condition can be tested at each point in the satisfies a predetermined trigger condition tree. but nothing otherwise. Binary options are also known as digital or all-or-nothing BLACK-DERMAN-TOY MODEL options. A one-factor log-normal interest rate model There are two major forms: at maturity and where the single source of uncertainty is the one-touch. At maturity binaries, also -term rate. The inputs into the model are known as European binaries or at expiry the observed term structure of spot interest binaries, pay out only if the spot trades rates and their volatility term structure. The above (or below) the trigger level at expiry. Black-Derman-Toy model, such as the Ho- One-touch binary options, also known as Lee model, describes the evolution of the American binaries, pay out if the spot rate entire term structure in a discrete-time trades through the trigger level at any time binomial tree framework. The model can be up to and including expiry. The pay-out of used to price bonds and interest rate- a one-touch binary may be due as soon as sensitive securities, though the solutions are the trigger condition is satisfied or not closed-form. alternatively at expiry (one-touch immediate or one-touch deferred binaries). As with barrier options, variations on the BLACK-SCHOLES MODEL theme include discrete binaries, stepped The original closed-form solution to option binaries, etc. pricing developed by Fischer Black and Binary options are frequently combined Myron Scholes in 1973. In its simplest form it with other instruments to create structured offers a solution to pricing European-style products, such as contingent premium options on assets with interim cash pay-outs options. over the life of the option. The model calculates the theoretical, or fair value for the option by constructing an instantaneously

5 Equity Derivatives Glossary

B/C riskless hedge: that is, one whose understood as the purchase of a call spread. performance is the mirror image of the See also bear spread, call spread option pay-out. The portfolio of option and hedge can then be assumed to earn the BUTTERFLY SPREAD risk-free rate of return. Central to the model is the assumption The simultaneous sale of a and that market returns are normally purchase of a money . The structure distributed (ie have lognormal prices), that profits if the underlying remains stable, and there are no transaction costs, that has limited risk in the event of a large move volatility and interest rates remain constant in either direction. As a trading strategy to throughout the life of the option, and that capitalise upon a range trading environment it the market follows a diffusion process. The is usually executed in equal notional model has five major inputs: the risk-free amounts. Alternatively, such trades are often interest rate, the option’s strike price, the applied to benefit from changes in volatility. In price of the underlying, the option’s such circumstances the butterfly spread is maturity, and the volatility assumed. Since traded on a ‘vega-neutral’ basis (ie the the first four are usually determined by the volatility sensitivity of the long position is market, options traders tend to trade the initially offset by the volatility sensitivity of the of the option. short position). As the holder of an initially vega-neutral spread, the trader will benefit from changes in volatility since the strangle BOND position profits more from an increase in Companies or governments issue bonds volatility than the straddle and loses less than as a means of raising capital. The bond the straddle in a decline in volatility (this is purchaser is in effect making a loan to the due to the fact that the vomma of the strangle issuer, and unlike with shares investors at is higher than that of the straddle). no point hold a stake in the company.

BOND INDEX SWAP A swap in which one counterparty receives C the total rate of return of a or segment of a bond market in exchange for paying a money market rate. Counterparties may also swap the returns A strategy that involves buying and selling of two bond markets. options or futures with the same (strike) price

but different maturities. Such a strategy is BOX used in futures when one contract month is To buy/sell mispriced options and hedge theoretically cheap and another is expensive. the using only options, unlike With options, the strategy is often used to the conversion or the reversal, which use play the shape of or expected changes in, the futures contracts. If a certain strike put is volatility term structure. For example, if one- underpriced, the trader buys the put and month volatility is high and one-year volatility sells a call at the same strike, creating a low, arbitrageurs might buy one-year synthetic short futures position. To get rid and sell short-term straddles, of the market risk, he sells another put and thereby selling short-term volatility and buys another call, but at different strike buying long-term volatility. If, all else being prices. See also convergence trade equal, short-term volatility declines relative to long-term volatility, the strategy makes money. BRACE-GATAREK-MUSIELA (BGM) MODEL

See market model of interest rates. BULL SPREAD

An option spread trade that reflects a bullish view on the market. It is usually

6 Equity Derivatives Glossary

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CALL OPTION protected if they rise. They are priced as the See option sum of the cost of the individual options, known as caplets. See also collar CALL SPREAD CAPITAL-PROTECTED A strategy that reduces the cost of buying a by selling another call at a A that provides capital higher strike price (Bull call spread). This protection offers an amount that at least limits potential gain if the underlying goes matches a given proportion of the investor’s up, but the premium received from selling original capital input at maturity. Can also be the out-of-the-money call partly referred to as principal-protected. Capital- the at-the-money call. A call spread may protected credit-linked note A credit-linked be advantageous if the purchaser thinks note where the principal is partly or fully there is only limited upside in the guaranteed to be repaid at maturity. In a underlying. Alternatively a Bear call spread 100% principal-guaranteed credit-linked note, can be constructed by selling a call option only the coupons paid under the note bear and buying another at a higher strike price. credit risk. Such a structure can be analysed See also bear spread, bull spread, put as (i) a Treasury strip and (ii) a stream of spread risky annuities representing the coupon, purchased from the note proceeds minus the cost of the Treasury strip. See also credit- CALLABLE SWAP linked note An interest rate swap in which the fixed- rate payer has the right to terminate the CAPPED FLOATER swap after a certain time if rates fall. Often done in conjunction with callable debt A floating-rate note which pays a coupon only issues where an issuer is more concerned up to a specified maximum level of the with the cost of debt than the maturity. The reference rate. This is done by embedding a is, in effect, a swaption cap in a vanilla note where the investor sold by the fixed-rate receiver which effectively sells the issuer a cap. A capped enables the fixed-rate payer to receive the floater protects the debt issuer from large same high fixed rate for the remaining increases in the interest rate environment. years of the swap in the event that interest rates fall. The fixed rate received under CAPPED SWAP the swaption offsets the fixed rate paid An interest rate swap with an embedded cap under the original swap effectively in which the floating payments of the swap cancelling the swap. In some definitions of are capped at a certain level. A floating-rate a callable swap, the fixed-rate receiver has payer can thereby limit its exposure to rising the right to terminate the swap. Also interest rates. known as a cancellable swap.

CAPTION CANCELLABLE SWAP An option on a cap. A type of compound See callable swap option in which the purchaser has the right,

but not the obligation, to buy or sell a cap at a CAP predetermined price on a predetermined A contract whereby the seller agrees to date. Captions can be a cheap way of pay to the purchaser, in return for an leveraging into the more expensive option. upfront premium or a series of annuity See also floortion payments, the difference between a reference rate and an agreed strike rate CASH AND CARRY when the reference exceeds the strike. When a exists, the premium of the Commonly, the reference rate is three- or forward position over the spot generally six-month Libor. A cap is therefore a strip reflects costs of buying and holding (eg of interest rate guarantees that allows the financing, transaction costs, insurance, purchaser to take advantage of a reduction in interest rates and to be

7 Equity Derivatives Glossary

C custody) for that period. See also cash and carry arbitrage A chooser option offers purchasers the choice, after a predetermined period, CASH MARKET between a put and a call option. The pay-outs are similar to those of a straddle but chooser The physical market for buying and selling options are cheaper because purchasers an underlying (eg equities, bonds), as must choose before expiry whether they want opposed to a futures market. the put or the call.

CASH-AND-CARRY ARBITRAGE CLIQUET

Cliquet structures, which can also be called A strategy, used in bond or stock index ratchet structures, periodically settle and futures, in which a trader sells a futures reset their strike prices, allowing users to contract and buys the underlying to deliver lock-in potential profits on the underlying. into it, to generate a riskless profit. With a cliquet the payout is worked out from For the strategy to work, the futures the performance of the underlying asset in a contract must be theoretically expensive number of set periods during the product’s relative to cash. life. See also ladder options Cash-and-carry arbitrage and reverse cash-and-carry arbitrage typically keep the futures and underlying markets closely aligned. See also basis trading, reverse Also known as a ratchet or reset option. A cash-and-carry arbitrage path-dependent option that allows buyers to lock-in gains on the underlying security CATASTROPHE BOND during chosen intervals over the life time of the option.The option’s strike price is A bond that pays a coupon that decreases effectively reset on predetermined dates. only after a catastrophe such as a Gains, if any, are locked in. So if an hurricane or earthquake with a specified underlying rises from 100 to 110 in year one, magnitude in a specified region and period the buyer locks in 10 points and the strike of time. price is reset at 110. If it falls to 97 in the next

year the strike price is reset at that lower CATASTROPHE OPTION level, no further profits are locked in, but the These options can be American-style or accrued profit is kept. See also ladder option, European-style, either paying out if a , moving strike option, path single specified catastrophe such as a dependent option hurricane or earthquake occurs, or alternatively, having a pay-out dependent CLOSED-FORM SOLUTION on an index. For example, the index may Also called an analytical solution. An explicit represent the number of claims received solution of, for example, an option pricing by property insurance companies. problem by the use of formulae involving only

simple mathematical functions, such as CATASTROPHE RISK SWAP Black-Scholes or Vasicek models. Closed- An agreement between two parties to form models can usually be evaluated much exchange catastrophe risk exposures. For more quickly than numerical models, which example, in July 2001 Swiss Re and are sometimes far more computationally Tokyo Marine arranged a $450 million deal intensive. including three risk swaps: Japan earthquake for California earthquake, COLLAR Japan typhoon for France storm and The simultaneous sale of an out-of-the- Japan typhoon for Florida hurricane. money call and purchase of an out-of-the- Swaps increase diversification and allow money put (or cap and floor in the case of each of the parties to lower the amount of interest rate options).The premium from capital that they need to hold. selling the call reduces the cost of purchasing

8 Equity Derivatives Glossary

C the put. The amount saved depends on so reduce its required capital reserves, while the strike rate of the two options. If the retaining contact with the borrowers and fees premium raised by the sale of the call from servicing the loans. See also exactly matches the cost of the put, the collateralised mortgage obligation strategy is known as a zero cost collar. COLLATERALISED MORTGAGE OBLIGATION The combination of purchasing the put and selling the call while holding the underlying A type of asset-backed security, in this case protects the holder from losses if the backed by mortgage payments. underlying falls in price, at the expense of Typically, such securities provide a higher giving away potential upside. See also return than normal fixed-rate securities but cap, equity collar, impact forward, risk purchasers suffer prepayment risk if reversal, zero cost option mortgage holders redeem their mortgages. Because the right to redeem the mortgage is effectively an embedded call, such securities COLLAR SWAP have negative convexity. See also A collar on the floating-rate leg of an collateralised bond obligation, collateralised interest rate swap. The transaction is zero debt obligation, collateralised loan obligation cost – the purchase of the cap is financed by the sale of the floor. The collar COMBO constrains both the upside and the downside of a swap. See

COLLARED FLOATER A floating-rate note whose coupon A compound option is an option on an option. payments are subject to an embedded The tool allows the user to buy or sell an collar. Thus the coupon is capped at a option at a fixed price during a set period. predetermined level, so the buyer forsakes They are often used to hedge against some upside, but also floored, offering increase in option prices during volatile protection from a downturn in the periods. Examples include captions and reference interest rate. Also known as a floortions. mini-max floater. CONDOR COLLATERALISED BOND OBLIGATION (CBO) The simultaneous purchase (sale) of an out- A multi-tranche debt structure, similar to a of-the-money strangle and sale (purchase) of collateralised mortgage obligation. But an even further out-of-the-money strangle. rather than mortgages, low-rated bonds The strategy limits the profit or loss of the serve as the collateral. See also pay-out and is directionally neutral. collateralised mortgage obligation COLLATERALISED DEBT OBLIGATION (CDO) This is an interest rate swap where the Generic name for collateralised bond floating interest arm is reset periodically with obligations, collateralised loan obligations, reference to longer duration treasury-based and collateralised mortgage obligations. instruments rather than a market index such See also collateralised mortgage as LIBOR. obligation, synthetic collateralised debt obligation CONSTANT MATURITY TREASURY DERIVATIVE Over-the-counter swaps and options which COLLATERALISED LOAN OBLIGATION (CLO) use longer-term, Treasury-based instruments A structured bond backed by the loan for their floating rate reference than money repayments from a portfolio of pooled market indexes, such as Libor.‘Constant personal or commercial loans, excluding Maturity Treasury’ (CMT) refers to the par mortgages. The structure allows a bank to yield that would be paid by a treasury bill, remove loans from its balance sheet and note or bond which matures in exactly one, two, three, five, seven, 10, 20 or 30 years.

9 Equity Derivatives Glossary

Since there may not be treasury issues in perform well and decreased when these the market with exactly these maturities, perform poorly. the yield is interpolated from the yields on The capital protection level may be fixed, or treasuries that are available. In the US, rachet up (reset) according to a certain such rates have been calculated and percentage of the fund NAV achieved during published by the Federal Reserve Bank of the fund term. New York and the US Treasury department on a daily basis every day for CONTINGENT SWAP more than 30 years. The H.15 Report from the Federal Reserve Bank is often used as The generic term for a swap activated when a source for CMT rates. rates reach a certain level or a specific event It is then possible for this interpolated yield occurs. Swaptions are often considered to be to form the index rate for instruments such contingent swaps. Other types of swaps, for as floating rate notes, which pay interest example, drop-lock swaps, are activated only linked to the CMT yield, options, which pay if rates drop to a certain level or if a specified the difference between a strike price and level over a benchmark is achieved. the CMT yield, and swaps and swaptions, in which one of the cashflows exchanged (CFD) is the CMT yield. Where necessary, the A Contract for Difference is typically an reference rate is reset at each settlement agreement made between two parties to date. Typical uses of CMT derivatives as exchange (at the closing of the contract) a hedging tools include the purchase of cashflow equivalent to the difference between CMT floors by mortgage servicing the opening and closing prices, multiplied by companies to protect the value of the number of shares detailed in the contract. purchased mortgage servicing portfolios, CFDs are traded on , do not incur and the purchase of CMT caps to protect stamp duty and can have individual or investors with negatively convex indexes as the underlying. mortgage-backed securities portfolios. It is possible to enter into derivatives in other currencies that are based, by analogy, on CONVERGENCE TRADE a ‘constant maturity interest rate swap’ Trading strategy where similar securities are interpolated from the swap curve in the bought and sold simultaneously in the relevant currency. Such derivatives are expectation that prices will converge in an known as constant maturity swap (CMS) orderly fashion. derivatives. Unlike CMT derivatives, CMS 1.A way of taking advantage of mispriced derivatives incorporate the spread options by creating a synthetic short futures component of swaps. position and hedging market risk by buying a futures contract against it. Thus if a put is CONSTANT PROPORTION PORTFOLIO undervalued, a trader buys it, at the same INSURANCE (CPPI) time selling a fairly valued call and buying a futures contract. The same strategy can be A fund management technique that aims applied if the call is mispriced. If the option is to provide maximum exposure to risky truly undervalued, the trader earns a riskless assets while still protecting investors’ profit. The whole exercise relies on put-call capital. The technique requires the parity manager to dynamically rebalance the 2.The act of converting a portfolio between risky assets (such as into equity. See also box, reversal equities) and safe assets (such as bonds) according to a quantitative model. The level of risky assets is managed such that CONVERTIBLE BOND at all times, in the event of a market crash, A bond issued by a company that may be the remaining NAV of the fund is still exchanged by the holder for a number of that sufficient to meet the stated protection company’s shares at a predetermined ratio, level. Generally the proportion of Risky or at a discount to the share price at maturity. Assets in the fund is increased when these Because the convertible embeds a call option on the company’s equity, convertibles carry

10 Equity Derivatives Glossary

C much lower rates of interest than correlation between them having a direct traditional debt and are therefore a cheap influence on the option price. For quantos way for companies to raise debt. The such as guaranteed options, problem for existing shareholders is that or differential swaps, the correlation effect is conversion dilutes the company’s the extent to which there is a relationship outstanding shares. Typically, bonds are between movements in the underlying and convertible into a company’s own stock. movements in the ex-change rate, which has There are however ‘third party a secondary effect on the price of the option. convertibles’, which convert into shares of 3.Correlation between markets is also used another company. See also equity to offset an option position in one market , resettable convertible bond against another with similar direction and volatility. Such a strategy might be used to CONVEXITY reduce cost – to avoid hedging the positions separately, or because implied volatility in the A bond’s convexity is the amount that its second market is lower – or because hedging price sensitivity differs from that implied by is difficult in the first market. Correlation can the bond’s duration. Fixed-rate bonds and be estimated historically (like volatility) but swaps have positive convexity: when rates tends to be unstable, and historic estimations rise the rate of change in their price is may be poor predictors of future realised slower than suggested by their duration; correlations. See also joint option when rates fall it is faster. Positive convexity is therefore a welcome attribute. The higher the bond’s duration, the more its convexity. Bonds or swaps with call An instrument that allows an investor to take options or embedded call options, eg financial exposure on a set of correlations. collateralised mortgage obligations, have negative convexity: when rates rise their CORRIDOR FLOATER price fall is faster relative to the interest rate move. Convexity effectively describes See range note the same attribute as gamma. CORRIDOR OPTION CORRELATION The holder of a corridor option receives a Correlation is a measure of the degree to coupon at the end of the lifetime of the which changes in two variables are corridor whose magnitude depends upon the related. It is normally expressed as a behaviour of a specified spot rate during the coefficient between plus one, which lifetime of the corridor. For each day on which means variables are perfectly correlated the spot rate (typically an official fixing rate (in that they move in the same direction to observation) remains within the chosen spot the same degree) and minus one, which range (the accrual corridor) the holder means they are perfectly negatively accrues one day’s worth of coupon interest. correlated (in that they move in opposite A variation is the knockout corridor option. In directions to the same degree). In financial this structure, the holder ceases to accrue markets correlation is important in three coupon interest as soon as the spot rate areas: leaves the range. Even if the spot rate 1.The model used for global asset subsequently re-enters the range, the holder allocation decisions, Sharpe’s capital does not continue to accrue coupon interest. asset pricing model (CAPM), has, as its At the end of the option’s lifetime, the linchpin, a covariance matrix that accrued coupon is calculated according to measures correlations between markets. the following formula: 2.Correlation is also central to the pricing If the accrual corridor is one-sided (the other of some options, where two-factor or side of the range bing open-ended), it is multi-factor models are used. For spread known as a wall option. Typically, corridor options, options and cross- options are imbedded in a structured note, currency caps, estimating the correlation sometimes called a range note, that pays a between the underlying assets is of higher yield than the corresponding vanilla primary importance, the degree of debt as long as the underlying rate remains

11 Equity Derivatives Glossary

C sufficiently long within the accrual corridor. increase the yield of the asset. Investors also A similar option to the corridor option is the sell covered puts if markets have fallen range binary, a binary option which pays a rapidly but seem to have bottomed, because fixed coupon amount if the range is not of the high volatility typically received on the breached but nothing if it is breached. option. See also

COST OF CARRY The cost of financing an asset. If the cost See warrant is lower than the interest received, the asset has a positive cost of carry; if higher, COX-INGERSOLL-ROSS MODEL the cost of carry is negative. The cost of carry is determined by the opportunities for In its simplest form this is a lognormal one- lending the asset and the shape of the factor model of the term structure of interest yield curve. So a bond, for example, would rates, which has the short rate of interest as have a positive cost of carry if short-term its single source of uncertainty. The model rates (financing rates) were lower than the allows for interest rate and is assets’s yield or (and) if the cost could be also known as the square root model mitigated by lending out the securities. because of the assumptions made about the See also future volatility of the short-term rate. The model provides closed-form solutions for prices of zero-coupon bonds, and put and call options COUNTERPARTY CREDIT RISK on those bonds. See credit risk CREDIT DEFAULT SWAP COVERED CALL A bilateral financial contract in which one To sell a call option while owning the counterparty (the protection buyer or buyer) underlying security on which the option is pays a periodic fee, typically expressed in written. The technique is used by fund basis points per annum on the notional managers to increase income by receiving amount, in return for a contingent payment by option premium. It would be used for the other counterparty (the protection seller securities they are willing to sell, only if the or seller) upon the occurrence of a credit underlying went up sufficiently for the event with respect to a specified reference option to be exercised. Generally, covered entity. The contingent payment is designed to call writers would undertake the strategy mirror the loss incurred by creditors of the only if they thought volatility was reference entity in the event of its default. overpriced in the market. The lower the The settlement mechanism may be cash or volatility, the less the covered call writer physical. See also basket credit default swap gains in return for giving up upside in the underlying. It provides downside protection only to the extent that the option premium offsets a market downturn. See also A bilateral financial contract, which isolates covered put credit risk from an underlying instrument and transfers that credit risk from one party to the contract (the protection buyer) to the other COVERED PUT (the protection seller). There are two main To sell a while holding cash. categories of credit derivatives: the first This technique is used to increase income consists of instruments such as credit default by receiving option premium. If the market swaps in which contingent payments occur goes down and the option is exercised, the as a result of a credit event; the second, cash can be used to buy the underlying to which includes options, seeks cover. Covered put writing is often used as to isolate the credit spread component of an a way of target buying: if an investor has a instrument’s market yield. target price at which he wants to buy, he can set the strike price of the option at that level and receive option premium to

12 Equity Derivatives Glossary

C

CREDIT EVENT spread between two predetermined debt Any one of a specified set of events, issues on the maturity date. See also credit which, if occurring with respect to an spread option obligation of the reference entity specified in a credit default swap, will trigger CREDIT SPREAD OPTION contingent payments. Applicable events, An option on the credit spread between two which generally include bankruptcy, debt issues. The option will pay out the repudiation/moratorium, restructuring, difference between the credit spread at failure to pay, and cross-acceleration are maturity and a strike spread determined at determined by negotiation between the the outset. See also credit spread forward parties at the outset of a credit default swap. CREDIT-LINKED NOTE CREDIT OPTION A security with redemption and/or coupon payments linked to the occurrence of a credit Put or call options on the price of either event with respect to a specified reference (a) a , bond, or loan, or entity. In effect, a credit-linked note embeds a (b) an asset swap package, consisting of a credit default swap into a funded asset to credit-risky instrument with any payment create a synthetic investment that replicates characteristics and a corresponding the credit risk associated with a bond or loan derivative contract that exchanges the of the reference entity. Credit-linked notes cashflows of that instrument for a floating are typically issued on an unsecured basis rate cashflow stream, typically three- or directly by a corporation or financial six-month Libor plus a spread. institution. Credit-linked notes may also be

issued from a collateralised Special Purpose CREDIT RISK Vehicle (SPV). See also capital-protected Also known as default risk. In broad terms, credit-linked note the risk that a loss will be incurred if a counterparty to a (derivatives) transaction CROSS-CURRENCY CAP does not fulfil its financial obligations in a A cap in which the vendor will pay the timely manner. The term is sometimes purchaser the spread between interest rates loosely used as shorthand for the (usually Libor-based) in different currencies likelihood or probability of default, minus a strike spread, where this exceeds irrespective of the value of any position zero, in return for a premium. It has the same exposed to this risk. More precisely, credit relationship to a differential swap as a cap risk is the risk of financial loss arising out has to an interest rate swap. See also cross- of holding a particular contract or portfolio. currency floor

CREDIT SPREAD CROSS-CURRENCY FLOOR A credit spread is the difference in yield This is an option setting a cap on the spread between two debt issues of similar between two index interest rates in different maturity and duration. The credit spread is currencies. See also cross-currency cap often quoted as a spread to a benchmark floating-rate index such as Libor, or alternatively as a spread to a highly rated CROSS- reference security such as a government A cross-currency swap involves the security. The credit spread is often used exchange of cashflows in one currency for as a measure of relative creditworthiness, those in another. Unlike single-currency with reduction in the credit spread swaps, cross-currency swaps often require reflecting an improvement in the an exchange of principal. Typically the borrower’s perceived creditworthiness. notional principal is exchanged at inception at CREDIT SPREAD FORWARD the prevailing spot rate. Interest rate payments are then passed back on a fixed, A cash-settled forward contract with settlement amounts based on the credit

13 Equity Derivatives Glossary

C/D floating or zero basis. The principal is then CURRENCY OVERLAY re-exchanged at maturity at the initial spot See overlay rate. CUMULATIVE CAP CURRENCY PROTECTED OPTION A cumulative interest rate cap protects The same as guaranteed exchange rate or against increases in total interest expense quanto option. over a specified period of time. This period C of time will incorporate several rate URRENCY RISK settings in determining the final interest Currency risk arises from changes in the expense (for example, four three-month value of currencies. For example, if a Libor settings for an annual interest company receives a portion of its income in a expense amount). This differs from a foreign currency, it is exposed to changes in standard cap, which caps an absolute rate the value of that currency. Risk management of interest in each calculation period. and derivatives can be used to minimise this Because a cumulative cap does not risk. provide the period-to-period protection of a standard cap, it is generally cheaper than CURRENCY STRUCK OPTION the corresponding standard cap. This is the same as joint option.

CURRENCY FORWARD CURRENT EXPOSURE An agreement to exchange a specified amount of one currency for another at a Another name for replacement cost. future date at a certain rate. The exchange of currencies is priced so as to allow no CYLINDER risk-free arbitrage. In other words, pricing See risk reversal is not a market estimate of the spot rate at that date, but is made according to the two currencies’ respective interest rates. For example, assuming that Eurosterling interest rates are 10% and Eurodollar 5%, D and the US dollar/sterling spot rate is 1.75, the forward rate should reflect the 5% interest rate advantage of depositing DEFERRED PAYOUT OPTION money in sterling. Thus the 12-month A deferred payout option is a variation on forward rate should be 1.6695. American-style options similar to a shout Forwards are more appropriate than option. The holder of the option may exercise options if a company has a strong it at any time, for the value taken by the directional view of expected movements in underlying at that time, but the payout is exchange rates. But certainty is rare and delayed until the expiry date. This term is hedging entirely with forwards may leave a also applied to certain digital options whose company locked into unfavourable payout is not paid when triggered, but exchange rates. Unlike options, forwards deferred until the final maturity. See also do not enable companies to take option styles advantage of favourable currency movements. The purchaser of a forward, unlike the purchaser of a future, carries DEFERRED START OPTION the credit risk of the firm from which it See makes the purchase. Since the contracts are not easily reassignable, it is difficult to D reduce this risk. ELAYED RESET SWAP Also known as an in-arrears swap. A swap in which floating payment is based on the future, rather than present, value of the reference rate. For six-month delayed Libor reset swaps, for example, instead of fixing

14 Equity Derivatives Glossary

D

Libor six months and two days before the convertible bonds. In mathematical models of payment date, the floating-rate borrower financial markets, derivatives are known as delays fixing until two days before contingent claims. payment. Such swaps are popular in a DIFFERENCE OPTION steep yield curve environment, when a fixed-rate receiver may think rates will not See spread option rise as fast as the yield curve predicts. DIFFUSION PROCESS DELTA A continuous-time model of the behaviour of The delta of an option describes its a random variable. An example of such a premium’s sensitivity to changes in the model is Generalised price of the underlying. In other words, an (GBM), which is often used to model the option’s delta will be the amount of the behaviour of spot rates. underlying necessary to hedge changes in the option price for small movements in DIGITAL OPTION the underlying. The delta of an option Digital options pay a set amount if the changes with changes in the price of the underlying asset is above, or sometimes underlying. An at-the-money option will below, a certain level on a specific date. have a delta of close to 50%. It falls for These options have only two possible out-of-the-money options and increases outcomes: a set payout, or nothing at all. for in-the-money options, but the change is Thus, they are also known as binary or all-or- non-linear: it changes much faster when nothing options. the option is close-to-the-money. The rate of change of delta is an option’s gamma. DIGITAL SWAP DELTA HEDGING A swap in which the fixed leg is only paid on each swap settlement date if the underlying An option is said to be delta-hedged if a has met certain trigger conditions over the position has been taken in the underlying period since the previous payment date. in proportion to its delta. For example, if Nothing is paid if this is not the case. The one is short a call option on an underlying premium for such a swap is amortised over with a face value of $1 million and a delta the maturity of the swap and an instalment of 25%, a long position of $250,000 in the paid at each payment date. underlying will leave one delta-neutral with no exposure to small changes in the price of the underlying. Such a hedge is only DISCRETE BARRIER OPTION effective instantaneously, however. Since the delta of an option is itself altered Barrier options where the trigger level is only by changes in the price of the underlying, active for part of the option’s lifetime. This interest rates, the option’s volatility and its includes barrier options where the trigger is time to expiry, changes in any of these only valid on certain fixing dates, as well as factors will shift the net position away from cases where the trigger is valid for sub- delta-neutrality. In practice, therefore, a intervals of the option’s lifetime. See also delta-hedge must be rebalanced barrier option continuously if it is to be effective. See also static replication DISTRIBUTION

The probability distribution of a variable DERIVATIVE describes the probability of the variable A derivative instrument or product is one attaining a certain value. Assumptions about whose value changes with changes in one the distribution of the underlying are crucial to or more underlying market variables, such option models because the distribution as equity or commodity prices, interest determines how likely it is that the option will rates or foreign exchange rates. Basic be exercised. Many models assume the derivatives include: forwards, futures, logarithm of the relative return has a normal swaps, options, warrants and distribution, which can be described by two

15 Equity Derivatives Glossary

D/E parameters. The first is the distribution’s mean; the second its standard deviation E (equivalent, if annualised, to volatility). In practice, most empirically observed asset distributions depart from normality. This departure can be described in terms of the EMBEDDED OPTION skew (how much it tilts to one side or the An option, often an , other) and , which describes how embedded in a debt instrument that affects its fat or thin are the tails at either side. Most redemption. Examples include mortgage- markets tend to have fat tails (to be backed securities and callable and puttable leptokurtic) rather than thin tails bonds. (platykurtic). This pushes up the price of E out-of-the-money options. MBEDDED OPTIONS do not have to be interest rate options; some are linked to the price of an equity index DOUBLE BARRIER OPTION (Nikkei 225 puts embedded in Nikkei-linked This is an option with two barriers; one bonds) or a commodity (usually gold). Many setting the upper limit of the price of the so-called guaranteed products contain zero- underlying and one setting the lower limit. coupon bonds and call options. If the underlying crosses either of these barriers the option is either activated E (knock-in) or deactivated (knock-out). See QUILIBRIUM MODEL also barrier option. A model that specifies processes for the underlying economic variables and the extra risk premium investors require for risky DOUBLE NO-TOUCH assets. The evolution of asset prices and A double no-touch option pays a set their risk derived from the model thus amount as long as one of two specified specified. barrier levels are not broken during the life of the option. This tool is popular for usage E (INDEX) SWAP in relatively stable markets. QUITY A swap in which the total or price return on an equity index, equity basket or single equity DOWNSIDE RISK is exchanged for a stream of cashflows The risk the investor is exposed to if there based on a short-term interest rate index (or is a fall in the value of the underlying. another index). Equity swaps are a convenient structure for DUAL CURRENCY SWAP switching into or out of equity markets, particularly for those that prefer to avoid, or Dual currency swaps are currency swaps are not allowed to use, stock index futures. that incorporate the foreign exchange Like futures, the price of the swap is directly options necessary to hedge the interest related to the cost of carry, although there payments back into the principal currency may also be tax considerations. for dual currency bonds.

EQUITY COLLAR DYNAMIC HEDGING Equity collars are used by investors keen to See delta hedging reduce their downside risk. An equity collar is

formed by buying an equity put option with a

strike price below the current value of the

equity, at the same time as selling an equity

call option with a strike above the current

equity price. Thus a collar is imposed around the investor’s equity position. If the value of the underlying equity falls through the strike of the bought put, it can be exercised to limit losses. However, if the underlying stock rises

16 Equity Derivatives Glossary

E through the strike of the sold call, the performance of the least-performing asset in investor may have to deliver the equity at a predefined basket. The Everest structure the strike, thus foregoing potential may also pay coupons over its life. additional upside. See also collar EQUITY KNOCK-OUT SWAP These are just like convertible bonds. The An interest rate or cross-currency swap main difference is that these are typically that gets terminated (knocked-out) if a issued on stock, which is not the stock of the given stock or equity-index reaches a issuing firm. specified trigger level between inception and expiry. The knock-out can be EXCHANGE-TRADED OPTION unconditional once the pre-determined equity level is reached, or the client can be See option given the choice to cancel the swap should the trigger level be reached. EXERCISE See option EQUITY LINKED NOTE An equity linked note is a tool that is linked to a single equity, equity index or basket of Any option with a more complicated payout equities. They may or may not be principal structure than a plain vanilla put or call protected. option. The payout of a plain vanilla option is simply the difference between the strike price EQUITY WARRANT of the option and the spot price of the A warrant is a issued underlying at the time of exercise. For a by a bank or other financial institutions, European-style option, the exercise time is which is traded on a ’s always the expiry date; other option styles equity market. Warrants may be issued offer greater flexibility. over securities such as shares in a There are a number of ways in which an company, a currency, an index or a option payout can differ from that of a plain commodity. A call warrant gives the holder vanilla. The payout could also be a function the right (but not the obligation) to buy a of: given security at a given price known as ¦¦the difference between a strike and an the exercise price, on a given date, known average rate for the underlying (average as the expiry date. Conversely a put options) warrant gives the holder the right to sell ¦¦the difference between prices for two the security at the exercise price on the different underlyings (difference options, expiry date. These instruments are exchange options), the same underlying at sometimes known as covered warrants or different times (high-low options) derivative warrants. See also convertible ¦¦the correlation between two or more bond, warrant underlyings (outperformance options, outside barrier options) ¦¦the difference between a strike and the spot EUROPEAN-STYLE OPTION rate at some time other than expiry (deferred European-style options can only be payout options, shout options, lookback exercised on their expiry date. They stand options, cliquet options, ladder options) in contrast to American-style options, ¦¦a fixed amount (binary options) which can be exercised at any time until Alternatively, or additionally, a payout may be maturity. conditional on certain trigger conditions being met. For example, barrier options are EVEREST STRUCTURE activated or nullified if a spot rate falls or rises through a predetermined trigger level. A capital guaranteed structure generally Multiple trigger conditions are possible (as in offering the investor the sum invested at the case of corridor or mini-premium options). maturity and potential upside linked to the

17 Equity Derivatives Glossary

E/F

EXPLODED TREE at least equal to the sum invested, plus some A tree (binomial or trinomial) in which an additional upside based on the performance up step followed by a down step gives a of the . However, unlike different outcome to a down step followed guaranteed funds, very few floor funds come by an up step. Consequently, the number with a contractual guarantee. Many floor of nodes increases exponentially, funds are managed using the technique of compared with a recombining tree, in constant proportion portfolio insurance which the number increases quadratically. (CPPI). This makes their evaluation exceptionally computer-intensive. The advantage is that FLOORTION they can be used to price path-dependent An option on a floor. The purchaser has the options and they are important for right, but not the obligation, to buy or sell a modelling interest rate options. floor at a predetermined price on a

predetermined date. See also caption EXTREME VALUE THEORY An area of statistical research that focuses FORWARD on modelling the extreme values of return See future distributions. This is important in finance because many models (for example the Black-Scholes Model) assume that the distribution of returns is log-normal. A forward rate agreement (FRA) allows However, real-world distributions are purchasers/sellers to fix the interest rate for a found to have fat-tails – implying that rare specified period in advance. One party pays events such as crashes are more likely fixed, the other an agreed variable rate. than the traditional theories suggest. Maturities are generally out to two years and are priced off the underlying yield curve. The transaction is done on a nominal amount and only the difference between contracted and F actual rates is paid. If rates have risen by the time of the agreement’s maturity, the purchaser receives the difference in rates from the seller and vice versa. A swap is F AT TAILS therefore a strip of FRAs. FRAs are off- See kurtosis balance sheet – there are no up-front or margin payments and the credit risk is limited FINANCIAL ENGINEERING to the mark-to-market value of the transactions. Unlike interest rate swaps, The design and construction of investment FRAs settle at the beginning of the interest products to achieve specified goals. period, two business days after the calculation date. FLEXIBLE OPTION A flexible option (also known as a flexible FORWARD START OPTION exchange or flex option) is a customisable An option that gives the purchaser the right to exchange-traded option, which allows the receive, after a specified time, a standard put buyer to customise contract terms such as or call option. The option’s strike price is set expiry date and contract size in addition to at the time the option is activated, rather than the strike price. Flexible options with single when it is purchased. The strike level is stock, index, or even currency underlyings usually set at a certain fixed percentage in or are traded on several major exchanges. out-of-the-money relative to the prevailing spot rate at the time the strike is activated. FLOOR FUND Also known as a ratchet fund. A particular type of structured product that aims to deliver minimum returns, which usually are

18 Equity Derivatives Glossary

F/G

FORWARD SWAP A swap in which rates are fixed before the G start date. If a company expects rates to rise soon but only needs funds later, it may enter into a forward swap. G AMMA FRATION The rate of change in the delta of an option for a small change in the underlying. The rate See interest rate guarantee of change is greatest when an option is at- the-money and decreases as the price of the FUTURE underlying moves further away from the strike price in either direction. A long gamma A future is a contract to buy or sell a position is one in which a trader is long standard quantity of a given instrument, at options. For a position that is short gamma, an agreed price, on a given date. A future the opposite holds. Gamma can be hedged is similar to a forward contract and differs by mirroring the options position. from an option in that both parties are Alternatively, a trader may choose to adjust obliged to abide by the transaction. the position in the underlying continually in Futures are traded on a range of order to maintain delta neutrality. See also underlying instruments including vega commodities, bonds, currencies and stock indexes. The most important difference between GARMAN-KOHLHAGEN MODEL futures and forwards is that futures are A model developed to price European-style almost always traded on an exchange and options on spot foreign exchange rates. The cleared by a clearing house, whereas model is based upon the Black-Scholes forwards are over-the-counter instruments. model with the addition of an extra interest Furthermore, futures, unlike forwards, rate factor for the foreign currency. have standard delivery dates and trading units. Most futures contracts expire on a G quarterly basis. Contracts specify either EARED BARRIER OPTION physical delivery of the underlying A type of in-the-money barrier option where the instrument or cash settlement at expiry. barrier is in-the-money and lies between the Cash settlement involves the company strike and the underlying spot rate. paying or being paid the difference between the price struck at the outset and GEARING the expiry price of the contract. See also cost of carry, implied repo rate Gearing refers to the degree of exposure of a product to movements in the underlying index. A product with 100% gearing would FUTURE RATE AGREEMENT have returns exactly equal to any rise in the See forward rate agreement index. A product’s gearing is also called participation. FUTURES OPTION G BROWNIAN MOTION An option, either a put or a call, on any EOMETRIC futures contract. Also known as an option Geometric Brownian motion is a model on a future. frequently used for the diffusion process followed by asset prices. Standard Brownian motion is a random walk process with Gaussian increments; that is, changes in the asset price are normally distributed. The term geometric means it is the proportional change in the asset price (as opposed to the absolute level) that is normally distributed. This gives the model useful properties, in that the asset price cannot be negative, and that the

19 Equity Derivatives Glossary

G logarithm of the asset price will be Quanto options can, however, look normally distributed, making the model cosmetically cheaper (or more expensive) analytically tractable. See also stochastic depending on the forward interest rates in the process two currencies. For example, buying a call on a US asset could be more expensive in euros GLOBAL FLOOR if there is a wide interest rate differential between the euro and the dollar. See also A term usually associated with cliquet joint option, quanto product products. A cliquet product with global floor will provide a minimum return that is at least equal to the principal invested. GUARANTEED FUND Some cliquet products can have A guaranteed fund comes with a promise by guaranteed principal redemption of more the guarantor to repay a portion, usually than 100%. 100% of the principal at maturity. Guaranteed funds can also incorporate guaranteed GROWTH PRODUCT coupons payable regardless of the underlying performance and/or non-guaranteed coupons A term used to describe a type of linked to the performance of underlying structured product whose payouts are only assets, often a stock index or basket of made at maturity with no income stream stocks.‘Guaranteed’ does not mean the during the product life. A growth product investment is risk-free. The guarantee on can be either principal guaranteed or non- principal repayment usually holds only when guaranteed, although the former is the product is held to maturity, and is subject common. to credit risk of the guarantor. Investors who redeem early are usually repaid at net asset GUARANTEE LEVEL value and thus subject to market risk. A The amount of principal that is guaranteed guaranteed fund is constructed by investing to be repaid at the maturity of the product. part of the proceeds in a zero-coupon bond or other instrument – which underwrites the guaranteed payment at GUARANTEED COUPON maturity – and the rest of the money in an Coupon payments that are guaranteed by embedded call or put option on the the guarantor, and are paid during the life underlying for additional returns. Hence, of the product irrespective of performance investors also run counterparty risk in relation of the underlying. to the option strategy. A guaranteed structure can also take the form of a guaranteed note or guaranteed bond. Generally, any GUARANTEED EXCHANGE RATE OPTION structured product with a promise to return An option (also known as a quanto option) 100% of the principal invested at maturity can on an asset in one currency denominated be considered a guaranteed product. in a second currency. The exchange rate at which the purchaser converts the GUARANTEED RETURN ON INVESTMENT currency is fixed at the start. Such options are popular as investors want exposure to Any instrument (usually a structured note) foreign assets without the foreign which guarantees investors a minimum return exchange risk. The extra cost of the option on their investment. This can be achieved by depends on the correlation between combining a debt issue with a structure, such movements in the exchange rate and as a collar or cylinder, which locks gains into movements in the underlying. The higher a range. This means that the investor gains (more positive) the correlation between the protection from an adverse market move by underlying and the exchange rate limiting participation in any favourable move. (expressed as the number of units of See also principal-guaranteed product currency two per unit of currency one) the more expensive a call option will be and the cheaper a put option will be.

20 Equity Derivatives Glossary

H

investor with a long equity position might H compensate by buying put options to protect against a fall in equity prices. A hedge is also the term for the transactions made to effect

this reduction. HAIRCUT The excess of an asset’s market value HIGH-COUPON SWAP over either the loan for which it can serve A swap in which the fixed-rate payments are as adequate capital, or the regulatory above market rates. (Also known as a capital value. It can also refer to the premium swap.) dealer’s commission on a transaction.

HIGH-INCOME PRODUCT HARD PROTECTION A type of structured product that pays an A term sometimes used to refer to the income that is well above the rate of interest level of capital protection provided in a on conventional fixed-rate deposits. high-income type of structured product. A Generally, the higher the rate of return hard protection level of 90% means that so offered on a product, the higher the degree of long as the index or basket of shares is risk. above 90% of the starting level, the investor’s capital will not be at risk. HIGH-LOW OPTION HEATH-JARROW-MORTON MODEL A combination of two lookback options. A high-low option pays the difference between A multi-factor interest rate model, which the high and low of an underlying, such as a describes the dynamic of forward rate stock index. A speculative purchaser would evolution. An extension of the Ho-Lee be taking the view that the market would be model, the underlying is the entire term more volatile than the implied volatilities of structure of interest rates. The approach is both lookback options incorporated in the very similar to the original Black-Scholes structure. See also path-dependent option model: it does not model qualities such as the ‘price for risk’. The model requires two inputs: the initial HINDSIGHT OPTION yield curve and a volatility structure for the See lookback option forward. The volatility is only specified in a very general form. By choosing an H appropriate volatility function, it is possible ISTORIC RATE ROLLOVER to reduce HJM to simpler models such as A historic rate rollover allows an existing Ho-Lee, Vasicek, and Cox-Ingersoll-Ross. currency forward or spot position to be rolled The practical importance of the HJM forward without generating any intermediate model is that it provides a single coherent cash flows. Effectively the position is framework for pricing and hedging an reinstated for a new settlement date using a entire book of instruments (including new off-market forward rate based on the instruments such as caps and swaptions) historic rate. and is not excessively computationally intensive. Research building on HJM (such HISTORICAL VOLATILITY as the market model) has concentrated on widening its scope to remove the Historical volatility is a measure of the possibility of negative interest rates, volatility of an underlying instrument over a include more than one interest rate curve past period. Historical volatility can be used and incorporate default risk. as a guide to pricing options but isn’t necessarily a good indicator of future volatility. Volatility is normally expressed as HEDGE the annualised standard deviation of the log To hedge is to reduce risk by making relative return. transactions that reduce exposure to market fluctuations; for example, an

21 Equity Derivatives Glossary

H/I

HO-LEE MODEL IMPLIED DISTRIBUTION The first model that set out to model The probability distribution of returns for an movements in the entire term structure of asset, which is implied by options traded on interest rates, not just the short rate, in a that asset. The distribution is inferred by way that was consistent with the initially combining the variation of volatility with strike observed term structure. However, since price (see ) and the the model only has a single random factor, assumptions made about the distribution in it makes the simplifying assumption that the option pricing model. the volatility structure remains constant along the yield curve. Heath-Jarrow- IMPLIED FORWARD CURVE Morton later generalised this model, using a more general form of volatility and The forward curve implied by forward rate introducing continuous trading. In addition, agreements (derived from the par curve) of Ho-Lee allows for the possibility of various maturities. It is usually steeper than negative interest rates. the spot yield curve. The model was developed using a binomial tree, although closed-form IMPLIED REPO RATE solutions have now been found for The return earned by buying a cheapest-to- discount bonds and discount bond options. deliver bond for a bond futures contract and selling it forward via the futures contract. See HULL-WHITE MODEL also future An extension of the for interest rates, the main difference being IMPLIED VOLATILITY that mean reversion is time-dependent. The value of volatility embedded in an option Both are one-factor models. The Hull- price. All things being equal, higher implied White model was developed using a volatility will lead to higher vanilla option trinomial lattice, although closed-form prices and vice versa. The effect of changes solutions for European-style options and in volatility on an option’s price is known as bond prices are possible. vega. If an option’s premium is known, its implied volatility can be derived by inputting HYBRID PRODUCTS all the known factors into an option pricing Hybrid products are constructed from a model (the current price of the underlying, combination of interest rate, commodity, interest rates, the time to maturity and the equity, credit and currency derivatives. strike price). The model will then calculate the volatility assumed in the option price, which will be the market’s best estimate of the HYPOTHECATION future volatility of the underlying. See also The posting of collateral. option, volatility skew, volatility term structure

IN-ARREARS SWAP See delayed reset swap I I NCOME PRODUCT IMPACT FORWARD A term used for any type of structured product that provides a periodic payment of A collared forward, such as one in which income. The rate of income is often higher the purchaser buys a put and sells a call, than the general rate of interest available on both being out-of-the-money. The fixed-rate deposits and therefore there may premiums on the two options balance out, be a risk the initial capital invested will not b so the strategy is zero cost. See also returned in full. collar

22 Equity Derivatives Glossary

I

INDEX AMORTISING SWAP (IAS) strike cap is cheaper than a conventional An interest rate swap whose principal cap. amortises on the back of movements in an index, such as Libor or constant maturity INITIAL INDEX LEVEL treasuries. The fixed-rate receiver Most structured products incorporate payouts effectively grants an option to the fixed- that are linked to the movement of an rate payer to amortise the swap. The underlying index or share. This performance option is triggered by interest rate is measured relative to the level of the movements after an initial lock-out period. underlying recorded at the start of the The notional principal amortises as rates investment term, or the initial index level. fall or remains constant if rates remain the same. In return for granting the option, the fixed-rate receiver gets a yield above INTEGRATED HEDGE current fixed rates. IAS have been widely A hedge that combines more than one used by US regional banks in their distinct price risk. For example, crude oil is asset/liability management activities. By usually priced in US dollars. Therefore a using IAS, banks were able to obtain the producer of crude oil whose home currency is negative convexity of a mortgage-backed not the dollar (say, the euro) is exposed to security and avoid the risk of excessive both currency risk and the price risk for crude prepayments due to changes in consumer oil. One possible integrated hedge would be sentiment. But the fixed receiver is a single quanto option, which would hedge exposed to both falling and rising rates. If the price of crude oil in euro. As such, it rates fall, there is the possibility at each would depend heavily on the correlation (if interest date that some or all of the swap any) between the two markets. will be terminated, creating a reinvestment risk. If rates rise, the swap may run to INTEREST RATE CORRIDOR maturity, providing meagre income while floating rates soar. An interest rate corridor is composed of a An IAS fixed-rate receiver is selling long interest rate cap position and a short volatility to the payer for an enhanced interest rate cap position. The buyer of the yield. So the lower the volatility of the corridor purchases a cap with a lower strike index, the lower the option value and yield while selling a second cap with a higher pick-up. A subsequent fall in volatility strike. The premium earned on the second benefits the receiver because the cap then reduces the cost of the structure as likelihood that the swap will amortise a whole. The buyer of the corridor is decreases. IAS can be structured with protected from rates rising above the first negative or positive convexity and the cap’s strike, but exposed if they rise past the amortisation schedules and lock-out second cap’s strike. It is possible to limit this periods can be changed in order to liability by selling a knock-out cap rather than increase or decrease yields. Also known a conventional cap. The structure is then as an Indexed principal swap. See also known as a knock-out interest rate corridor. mortgage swap INTEREST RATE GUARANTEE INDEX ARBITRAGE An option on a forward rate agreement See stock index arbitrage (FRA), also known as a FRAtion. Purchasers have the right, but not the obligation, to purchase an FRA at a predetermined strike. INDEXED STRIKE CAP Caps and floors are strips of IRGs. A cap for which the payout level is indexed to the level of the reference rate. For INTEREST RATE SWAP example, such a cap might be struck at 7.5% as long as the reference rate An agreement to exchange net future remained below 9%, but rise to 8.5% if the cashflows. Interest rate swaps most reference rate exceeded 9%. An indexed commonly change the basis on which liabilities are paid on a specified principal.

23 Equity Derivatives Glossary

I/J

They are also used to transform the INTRINSIC VALUE interest basis of assets. In its commonest The amount by which an option is in-the- form, the fixed-floating swap, one money, that is, its value relative to the current counterparty pays a fixed rate and the price. Option premiums other pays a floating rate based on a comprise intrinsic value and time value. reference rate, such as Libor. There is no exchange of principal – the interest rate I payments are made on a notional amount. NVERSE FLOATER In floating-floating swaps the two The payments made on an inverse floating counterparties pay a floating rate on a rate note (‘floater’) decrease as the reference different index, such as three-month Libor interest rate increases, the reverse of the versus six-month Libor. typical case where the payments rise with the Swaps usually extend out as far as 10 reference rate. years, although 12–40 year maturities are The purchaser of an inverse floating rate note available in some liquid currencies. is in effect selling interest rate caps – this will However, the longer the maturity of the increase the coupon payments in a stable or swap, the less liquid it becomes and credit lower interest rate environment, but reduce risk increases. Credit enhancements such them should interest rates rise. Typically, the as mutual put options and collateral are payment is found by a fixed rate minus two used to ameliorate the credit risk of longer times the reference rate. The floater can be term swaps. Interest rate swaps provide further leveraged by using a multiplier higher users with a way of hedging the effects of than two. changing interest rates. For example, a company can convert floating-rate interest payments to fixed-rate payments if it thinks interest rates will rise (which would make J its liabilities more expensive). Companies can also use interest rate swaps in conjunction with new debt issuance, raising money on, say, a fixed basis and JOINT OPTION swapping it into floating-rate debt. In an An option on an underlying, often a stock interest rate swap there is a fixed-rate index, denominated in a second currency. payer (floating-rate receiver) and a fixed- Unlike a guaranteed exchange rate option, in rate receiver (floating-rate payer). which exchange rates are fixed, the purchaser of a joint call option benefits from INTEREST-RATE CAP upside in the currency in which the asset is originally denominated, for example, S&P See cap 500 call option struck in euro. In this case, at the inception, strike is specified in euro. At IN-THE-MONEY the maturity, S&P 500 level is observed and Describes an option whose strike price is is multiplied by then current euro/US dollar advantageous compared with the current rate. This converted value of S&P 500 is forward market price of the underlying. compared with the strike to determine the The more an option is in-the-money, the payout in euro. See also correlation, higher its intrinsic value and the more guaranteed exchange rate option, quanto expensive it becomes. As an option product becomes more in-the-money, its delta increases and it behaves more like the underlying in profit and loss terms; hence One of the key assumptions of the Black- deep in-the-money options will have a Scholes model is that the asset price follows delta of close to one. See also at-the- geometric Brownian motion with constant money, out-of-the-money volatility and interest rates. In a jump diffusion model, it is assumed that, in addition to this regular diffusion, there are jumps in the market. This type of model is sometimes

24 Equity Derivatives Glossary

J/K/L used for modelling equities and emerging assume perfect normal distribution – produce market currencies. pricing biases for deep in- or out-of-the- money options.

K L

KICKER A kicker is a bonus payment that is LADDER OPTION sometimes made when a structured A path-dependent option, most often based product matures if the value of the on an equity index or a foreign exchange underlying asset has risen enough. rate. The payout of a ladder option increases stepwise as the underlying trades upwards KNOCK-IN (or downwards) through specified barrier levels (the ‘rungs’ of the ladder). Each time Products which knock-in begin working the underlying trades through a new barrier when the underlying passes through a level, the option payout is locked-in at the predetermined spot rate or barrier level. higher level. See also cliquet, cliquet option, Knock-in options are a kind of barrier lookback option option.

LAMBDA KNOCK-OUT A measure of the effective of an Products which knock-out terminate when instrument. It is defined as the percentage spot passes through a predetermined change in the market value of a derivative for barrier level. a one-percent move in the underlying. Unlike Knock-out options are a kind of barrier gearing, the lambda value captures the option. instrument’s delta. See also leverage

KNOCK-OUT INTEREST RATE CORRIDOR LEASE RATE SWAP A corridor in which a client purchases a Similar to an interest rate swap, a lease rate standard cap with a lower strike and sells swap is a fixed-for-floating agreement in a knock-out cap with a higher strike (rather which gold is borrowed/ lent at a "fixed" rate. than selling a conventional cap). This The floating leg is re-priced at incremental means that the client is protected from an time periods over the maturity of the swap. At increase in interest rates up to the strike the end of each floating period the agreed level for the knock-out cap, but exposed if upon benchmark lease rate is compared to rates rise beyond that level. However, the the contract rate and the party in debit pays client is protected once again if the rates the differential. The floating component is rise above the knock-out level, as the then rolled out for a further period. short knock-out cap will then be extinguished. LEGAL RISK KURTOSIS Legal risk arises from the risk of not legally being able to enforce contracts. It can be a A measure of how fast the tails or wings of particular issue in emerging markets where a probability distribution approach zero, derivatives regulations are still being evaluated relative to a normal distribution. developed. The tails are either fat-tailed (leptokurtic) or thin-tailed (platykurtic). Markets are generally leptokurtic. The fatter the tails, LEPTOKURTOSIS the greater the chance a variable will See kurtosis reach an extreme value, implying that models such as Black-Scholes – which

25 Equity Derivatives Glossary

L

LEVERAGE LIQUIDITY RISK The ability to control large amounts of an The risk associated with transactions made in underlying variable for a small initial illiquid markets. Such markets are investment. Futures and options are characterised by wide bid/offer spreads, lack regarded as leveraged products because of transparency and large movements in the initial premium paid by the purchaser price after a deal of is generally much smaller than the nominal any size. A firm wishing to unwind a portfolio amount of the underlying. Leverage is of illiquid instruments (for example, highly usually measured as a quantity called tailored structured notes) may find it has to lambda. See also lambda sell them at prices far below their fair values, exacerbating the problems that prompted the LEVERAGED INVERSE FLOATER decision to unwind.

See also inverse floater LISTED OPTION LIBOR See warrant, option

The London inter-bank offered rate (LIBOR) is the interest rate charged on LITE OPTION short-term interbank loans by banks A European-style basket option with a payout operating in London. The rate is set on a determined by the underlying assets that daily basis and is commonly used as a remain in the basket, after a certain number guide for the future level of interest rates. of the best and worst performing assets in the basket were removed at a specified date prior LIBOR-IN-ARREARS SWAP to expiry. Also known as an atlas option.

See delayed reset swap LOCAL CAP LIMIT BINARY A local cap is the maximum return in each period of a cliquet option, which is used to See range binary work out the overall payout.

LINEAR BASKET CREDIT DEFAULT SWAP LOCAL FLOOR A basket credit default swap, where A local floor is the minimum return in each investors are exposed to multiple period of a cliquet option, which is used to reference entities as if they had entered help work out the overall payout. into a separate credit default swap contract with respect to each reference entity. LONGSTAFF-SCHWARTZ MODEL A two-factor model of the term structure of LINEAR EX-LINKED SWAP interest rates. It produces a closed-form solution for the price of zero coupon bonds An interest rate swap with a quasi-fixed and a quasi-closed-form solution for options coupon that varies with the movement of a on zero coupon bonds. The model is chosen spot foreign exchange rate over developed in a Cox-Ingersoll-Ross framework the life of the deal. These swaps can be with short interest rates and their volatility as structured to pay a higher (or lower) the two sources of uncertainty in the coupon if a given currency weakens (or equation. strengthens) after the outset of the deal. The observation dates for the forex component coincide with the Libor reset LOOKBACK OPTION dates for coupon calculation. These swaps Lookback options give the holder the right at can be structured with a leveraged forex expiry to exercise the option at the most exposure. favourable rate or price reached by the underlying over the life of the option. As with average options, the strike may be either

26 Equity Derivatives Glossary

L/M fixed or floating. With an optimal rate (or but the underlying exposure remains hedged price) lookback option, the strike is fixed at by the range forward. the outset and the option will pay out against the highest (for a call) or lowest MARGRABE OPTION spot (for a put) reached over the life of the option, irrespective of the spot at expiry. See outperformance option The option will usually be settled in cash. Since the option is likely to have a larger MARKET MODEL OF INTEREST RATES payout than the corresponding plain A special case of the Heath-Jarrow-Morton vanilla option, it commands a larger model due to Brace, Gatarek and Musiela in premium. The strike for an optimal strike which the term structure of interest rates is lookback option, on the other hand, is not modelled in terms of simple Libor rates fixed until expiry, when it is set to be the (which are lognormally distributed with highest (for a put) or lowest spot (for a respect to forward measure) rather than call) over the option’s life and exercised for instantaneous forward rates. This allows the cash or physical against the spot modeller to exclude the possibility of negative prevailing at expiry. See also cliquet interest rates from the model and obtain option, ladder option, path-dependent prices for caps, floors and swaptions option, shout option consistent with the Black-Scholes framework. LOW EXERCISE PRICE OPTION (LEPO) The model can be calibrated using readily A low exercise price option (Lepo) is a call available market data: forward or swap rates option with an exercise price set deep in- volatilities and correlations, and is particularly the-money. The limiting case, a zero suited to path-dependent instruments. exercise price option, is when the strike price is zero. It is virtually certain to be MARKET RISK exercised and the value and performance Exposure to a change in the value of some of its intrinsic value is effectively identical market variable, such as interest rates or to that of the underlying equity. foreign exchange rates, equity or commodity These features are designed to allow prices. For holders of a derivatives position, participation in the performance of an market risk may be passed through from a equity price where there are legal or change in the value of the underlying to the financial obstacles to purchasing the price of the derivatives, or may arise from underlying directly. If the Lepo is cash- other sources, such as implied volatility or settled, the buyer profits to the same time decay. extent as with a direct holding in the underlying, but without having to transact in it. However, a Lepo holder does not MARKET VALUE earn dividends or have voting rights over See replacement cost the equity.

MARK-TO-MARKET This is the value of a financial instrument according to current market rates. M MARTINGALE MANDARIN COLLAR A probabilistic interpretation of the payout of a ‘fair game.’ The expected gain at any point The Mandarin collar combines a range in the future is equal to the actual gain now. forward with the purchase of a range See also binary structure, such that should the spot stay within the prescribed range, the proceeds of the range forward are MEAN REVERSION enhanced by the payout amount of the The phenomenon by which interest rates and range binary. If either of the limits trades at volatility appear to move back to a long-run any time, the range binary is terminated, average level. Interest rates’ mean-reverting

27 Equity Derivatives Glossary

M tendency is one explanation for the (which can occur if the mortgage holder pays behaviour of the term structure of volatility. off the mortgage or defaults). Such swaps are Some interest rate models incorporate complicated because although the fixed-rate mean reversion, such as Vasicek and receiver receives a higher rate than on a Cox-Ingersoll-Ross, in which high interest normal swap, the amortisation of the principal rates tend to go down and low ones up. is not just a function of interest rates. The largest mortgage swap market is in the US; in MEDIUM-TERM NOTE (MTN) 1992 and 1993 prepayments accelerated because of historically low interest rates. See A medium-term note is a debt instrument also index amortising swap, reverse index with a maturity of between three and amortising swap seven years, which may pay fixed or variable coupons. These notes can be used to construct structured notes by MORTGAGE-BACKED SECURITY embedding derivatives to create structured See asset backed security coupons which appeal to investors. MOVING STRIKE OPTION MID-ATLANTIC OPTION An option in which the strike is reset over See Bermudan option time, such as an interest rate cap in which the strike is reset for the next period at the MONTE CARLO SIMULATION current interest rate plus a pre-agreed spread. See also cliquet option A method of determining the value of a derivative by simulating the evolution of the underlying variable(s) many times MULTI-FACTOR MODEL over. The discounted average outcome of Any model in which there are two or more the simulation gives an approximation of uncertain parameters in the option price (one- the derivative’s value. This method may be factor models incorporate only one cause of used to value complex derivatives, uncertainty: the future price). Multi-factor particularly path-dependent options, for models are useful for two main reasons. which closed-form solutions have not been Firstly, they permit more realistic modelling, or cannot be found. Monte Carlo particularly of interest rates, although they simulation can also be used to estimate are very difficult to compute. Secondly, multi- the value-at-risk (VaR) of a portfolio. In factor options (for example, spread options) this case, a simulation of many correlated have several parameters, each with market movements is generated for the independent volatilities, and also the markets to which the portfolio is exposed, correlation between the underlyings must be and the positions in the portfolio revalued dealt with separately. repeatedly in accordance with the simulated scenarios. The result of this MULTIPLE STRIKE OPTION calculation will be a probability distribution of portfolio gains and losses from which See outperformance option the VaR can be determined. The principal difficulty with Monte Carlo VaR analysis is MUNICIPAL SWAP that it can be very computationally A swap in which the floating payments are intensive. based on an index of tax-exempt US municipal bonds, such as J.J. Kenny. MORTGAGE SWAP An asset swap attached to fixed-rate mortgage payments. Mortgage swaps allow investors to enjoy the flows from a portfolio of mortgages without taking a mortgage asset on to their balance sheet. The principal reduces if and when the outstanding mortgage principal reduces

28 Equity Derivatives Glossary

N/O

synthetic forwards, which entail no exchange N of currencies at maturity. Instead, settlement is made in US dollars based on the difference between the agreed contract rate at inception

and a market reference rate at maturity. NAKED OPTION NDFs can be used to establish a hedge or An option that is sold (bought) without take a position in one of a growing group of holding the underlying or otherwise emerging market currencies where hedging. conventional forward markets either do not exist or may be closed to non-residents. As offshore instruments, NDFs offer the N ATURAL HEDGE advantage of eliminating convertibility risk, A natural hedge is the reduction in since no emerging market currencies are financial risk that can arise from an exchanged at maturity. institution’s normal operating procedures. For instance, a company that has a significant portion of its sales in one country will have a natural hedge to at O least part of its currency risk if it also has operations in that country generating expenses in the currency. Firms may act to increase natural hedges by changing ONE-FACTOR MODEL sourcing, funding, or operational A model or description of a system where the decisions, but natural hedges are less model incorporates only one variable or flexible, and more difficult to reverse, than uncertainty: the future price. These are financial hedges. simple models, usually leading to closed-form NEGATIVE BASIS solutions, such as the Black-Scholes model or the Vasicek model. Negative basis exists when the cost of buying protection (in the credit ) on a particular reference entity is OPEN-ENDED PRODUCT less than the credit spread (generally Structured products that can be used for expressed as a spread to Libor) on a bond investment for an unlimited period are or note of similar maturity issued by that sometimes called open-ended products. They reference entity. When this occurs, stand in contrast to tranche or close-ended investors can lock in riskless profit by products. buying bonds and buying credit protection. These arbitrage opportunities are O generally only available to investors whose PERATIONAL RISK cost of funds is Libor flat or better (since The risk run by a firm that its internal funding the bond or note at Libor plus a practices, policies and systems are not spread will erode the arbitrage). Technical rigorous or sophisticated enough to cope with factors between the bond and credit untoward market conditions or human or derivatives market account for negative technological errors. Although operational basis. risk is not as easy to identify or quantify as market or credit risk, it has been implicated NET PRESENT VALUE as a major factor in many of the highly- publicised derivatives losses of recent years. A technique for assessing the worth of Sources of operational risk include: failure to future payments by looking at the present correctly measure or report risk; lack of value of those future cashflows discounted controls to prevent unauthorised or at today’s cost of capital. inappropriate transactions being made (the so-called ‘rogue trader’ syndrome); and lack NON-DELIVERABLE FORWARD of understanding or awareness among key staff. Non-deliverable forward contracts (NDFs)

– also called dollar-settled forwards – are

29 Equity Derivatives Glossary

O

OPTION The extent to which an option is in-the-money A contract that gives the purchaser the (how far the strike price is below/above the right, but not the obligation, to buy or sell current forward market price) is called its an underlying at a certain price (the intrinsic value. Where the strike price is less exercise, or strike price) on or before an favourable than the market price, the option agreed date (the exercise period). is said to be out-of-the-money, and where the For this right, the purchaser pays a two prices are the same it is at-the-money. premium to the seller. The seller (writer) of At any time before maturity, an option’s price an option has a duty to buy or sell at the will be a combination of its intrinsic value strike price, should the purchaser exercise (which is always either greater than, or equal his right. With European-style options, to, zero) and its time value. The latter purchasers may take delivery of the includes the cost of carry and the probability underlying only at the end of the option’s that the price of the underlying will move into life. American-style options may be or remain in the money. Options can broadly exercised, for immediate delivery, at any be used in two ways – for speculation, or for time over the life of the option. Holders of insurance. Their usefulness, both from a semi-American-style or Bermudan options buyer’s and a seller’s point of view, derives may be exercised on specified dates – from their payouts. In contrast to other types typically on a monthly or quarterly basis. of hedge, options provide insurance against Options can be bought on commodities, unfavourable moves in a product’s price and stocks, stock indexes, interest rates, the opportunity to take advantage of bonds, currencies, etc. The trading favourable moves. Forwards and futures, for terminology, though, may change example, require buyers and sellers to lock according to the product. In most cases, into one rate. In return for assuming this risk, the right to buy the underlying is known as sellers of options receive a premium, a call, and the right to sell, a put. effectively a risk-taking fee. The payout of a Options are traded on formal exchanges purchased option means that the price risk of and in over-the-counter (OTC) markets. an option is limited to its premium – it is not The exchanges, such as the Hong Kong as exposed to adverse movements as a Stock Exchange, the SIMEX, or the ASX position in the underlying. provide primarily standardised options; the For speculators selling (writing) options, this OTC markets are able to provide tailored often means taking a naked option position products to fit specific requirements. The and therefore being exposed to adverse choice between OTC and exchange- movements in the underlying. Hedgers may traded options will depend on the degree sell options to garner premium to offset any of tailoring required, the relative liquidity of expected slight downturn in a market. Since both markets (this varies greatly according option premiums are only a fraction of the to the underlying) and credit concerns. cost of the underlying product, it is possible to Pricing models for simple or vanilla options achieve a much greater exposure to price have five major inputs: the option’s changes of the underlying compared with a exercise or strike price; the time to similar investment directly in the product – ; the price of the underlying this is called leverage. See also implied instrument; the risk-free interest rate on volatility the underlying instrument, and the volatility of the underlying instrument. OPTION COMBINATION STRATEGIES European-style options are usually priced Options may be combined so that their off a closed-form analytical model first payouts produce a desired risk profile. Some published by Fischer Black and Myron combinations are primarily trading strategies, Scholes in 1973, which has subsequently but option combinations can be useful in, for been modified to fit different underlying. example, allowing investors to construct a At maturity, an option’s value will depend strategy to take advantage of a particular on the value of the right to buy or sell a view they have of the market. Other product. If an option is purchased giving strategies allow purchasers to reduce their the right to buy gold at $375 an ounce and premiums by giving up some of the benefits at expiration the rice is $400, the option is they may have received from market worth $25.

30 Equity Derivatives Glossary

O/P movements. See also put spread, slimmer). Its delta also declines and it straddle, strangle becomes less sensitive to movements in the underlying. See also at-the-money, in-the- OPTION ON FUTURE money

See futures option OUTPERFORMANCE OPTION OPTION REPLICATION Also known as a Margrabe option. A two- factor option giving the purchaser the right to See replication receive the outperformance of one asset over another asset. For example, a purchaser with OPTION STYLES a view that the Hang Seng Index (HSI) will The purchaser of a European-style option outperform the Dow Jones Euro Stoxx 50 has the right to exercise it on a (Euro Stoxx) index should buy the predetermined expiry date. In contrast, the outperformance option, which pays notional holder of an American-style option has the multiplied by the outperformance of the HSI right to exercise it at any time during its index over the Euro Stoxx index. In this case, lifetime, up to and including its expiry date. the payout is zero if HSI underperforms Euro This flexibility means there is a greater Stoxx. The value of an outperformance option probability of an American-style option will largely be dictated by the historical being exercised than the corresponding correlation between the underlyings. European-style option with the same strike. Hence the early exercise feature of OVERLAY an American option adds value and makes A strategy to change the exposure of a it the more expensive of the two. Most portfolio using derivatives, while leaving the exchange-traded options are American- securities in the underlying portfolio style. Further variations on these styles unchanged. This has the advantage of cost also exist. A Bermudan option, so called and flexibility, as portfolio managers can because it falls between American- and adjust portfolio risk more quickly and cheaply European-style options, has more than with derivatives than by liquidating portfolio one possible exercise date. For example, holdings. Another reason might be tactical – the holder of a Bermudan option with a the adjustment may only be desired for a two-year maturity might have the right to brief period of perceived market threat. A exercise it every quarter or half year third reason might be to transform a portfolio during the life of the contract. Bermudans risk; an international fund manager may wish are also known as limited exercise or to segregate the currency aspect of a semi-American-style options. Another twist portfolio and can do so with a currency is the deferred payout option, a variation overlay programme. See also asset allocation on American-style options in which the option can be exercised at any time during the option’s life, but the payout is delayed OVER-THE-COUNTER (OTC) until the expiry date.With the similar shout Financial products that are not traded on option, the purchaser can lock in a profit at formal exchanges are said to be traded over- any time, but retains the right to profit from the-counter. further favourable moves. See also American-style option, Bermudan option, deferred payout option P OUT-OF-THE-MONEY Describes an option for which the forward market price of the underlying is below the PARISIAN BARRIER OPTION strike price in the case of a call, or above it A barrier option with a barrier that is triggered in the case of a put. The more the option is only if the underlying has been beyond the out-of-the-money, the cheaper it is (since barrier level for longer than a specified period the chances of it being exercised get

31 Equity Derivatives Glossary

P of time. See also barrier option, trigger, necessary. Usually, the holder will pay an trigger condition initial premium (which will be small compared with the premium for a normal cap) and a PARTICIPATING FORWARD further payment at each reset date. The holder can cancel the cap when he or she The simultaneous purchase of a call feels that the protection is no longer needed. option (put option) and sale of a put (call) A pay-as-you-go cap is useful for those who at the same strike price, usually for zero feel that caps are too expensive, that interest cost. The option purchased must be out- rates will eventually stabilise below the of-the-money and the option sold (to capped level, or that rates are in a short-lived finance the option purchase) is for a ‘spike’ move. Also known as an installment smaller amount and will be in-the-money. cap. See also zero cost option

PAYOUT/PAYOFF PARTICIPATING OPTION A general term used to describe the return An option whereby the buyer pays a provided by a structured product or an option. reduced premium but has to forgo a A lot of products pay a fixed coupon plus portion of his potential gains. additional returns linked to performance of the nderlying. If the embedded option is path- PARTICIPATING SWAP dependent, the returns will be a function of A swap in which floating-rate exposure is both the performance of the index and the hedged but in which the hedger still retains payout formula. For example, the payout from some benefit from a fall in rates. a five-year quarterly with a 70% participation of the Dow Jones Euro Stoxx 50 Index is equal to 70% of the average of 20 PARTICIPATION RATE different prices over five years, and not the Many structured products incorporate level of the index at maturity. returns at maturity that are calculated by multiplying the performance of the PERIOD RESETTING SWAP underlying (which can be an index, stock basket or fund) by a fixed percentage. This An interest rate swap in which the floating- percentage is called the participation rate. rate payments are an average of the floating For example, a 70% participation in the rates observed since the last payment. index means that 70% of the performance of the underlying index will be used to PERIODIC CAP calculate the maturity payout. If the A cap in which the strike rate can vary from product comes with a 100% capital period to period. The strike rate in a given guarantee, the participation rate will only period depends upon the strike set in the apply to the upside, not to index losses. previous period. Such caps are normally set at a fixed number of basis points above the PATH-DEPENDENT OPTION previous strike, or the index (for example, A path-dependent option has a payout Libor) plus a spread. Periodic caps can be directly related to movements in the price with or without "memory". A periodic cap of the underlying during the option’s life. without memory simply looks at the strike in By contrast, the payout of a standard the immediately preceding period to European-style option is determined solely determine a new strike, while one with by the price at expiry. See also barrier memory may look at previous settings in option, cliquet option, high-low option, determining the new strike. Periodic caps are lookback option, shout option common features in adjustable rate mortgages (ARMs) in the US where the borrower’s floating interest payments cannot PAY-AS-YOU-GO CAP go up by more than a set number of basis A pay-as-you-go cap allows the buyer to points in a given year. See also periodic floor pay for protection from upward moves in an interest rate for only as long as

32 Equity Derivatives Glossary

P

PERIODIC FLOOR POWER SWAP A floor in which the strike rate can vary A swap whose floating leg is based on the from period to period. The strike rate in a square (or some higher exponent) of the given period depends upon the strike set reference interest rate. Although dismissed in the previous period. Such floors are by some as little more than a speculative tool normally set at a fixed number of basis for taking highly leveraged positions on the points above the previous strike or the direction of interest rates, power swaps have index (for example Libor) plus a spread. been shown (by Robert Jarrow and Donald See also periodic cap van Deventer) to have their uses in hedging commercial banks’ deposits and credit card loan portfolios. See also power option

The phenomenon where a small move in the underlying can have a significant PREMIUM impact on the value of an at-the-money See option option shortly before expiration. PREMIUM-REDUCTION DEVICE PODIUM A strategy that aims to reduce the cost of an A type of correlation product that is fully option or other derivative. There are many capital-guaranteed, but with the annual ways to achieve this; three common coupons dependent upon the number of techniques follow. underlyings within the basket that meet The first is to sell a second derivative; the certain performance criteria. premium received can then be used to lower the funding requirement for the purchased PORTFOLIO OPTION derivative. This is the technique employed for reducing the cost of a collar. A portfolio option is a multi-factor option The second is to limit participation in moves that pays out the difference between the in the underlying by imposing limitations on return from a portfolio of assets and a the payout profile of the instrument (as in a specified strike price. barrier option or a capped floater). The final way is to accept payments below POSITIVE BASIS market rates, with the possibility of making up Positive basis exists when the cost of the shortfall at the end of the instrument’s life buying protection (in the credit derivatives (see yield adjustment). market) on a particular reference entity exceeds the credit spread (generally PRINCIPAL-GUARANTEED PRODUCT expressed as a spread to Libor) on a bond Any investment vehicle that allows investors or note of similar maturity issued by that to gain exposure to an asset while reference entity. When this occurs, guaranteeing the return of their principal, investors looking to gain exposure to the often at maturity only. Such products are reference entity can improve their normally constructed by buying a deep expected return on an investment by discount bond (often a zero-coupon bond) taking exposure to the credit by selling and using the rest of the money to buy protection in the credit derivatives market embedded call or put options to gain rather than buying the bond or note. exposure to a second asset, often a stock Technical factors between the bond and index. See also guaranteed return on credit derivatives market account for investment positive basis.

PROGRAM TRADING POWER OPTION A strategy to trade a basket of shares An option with a payout dependent on the simultaneously, normally by means of price of the underlying at expiry, raised to computer-generated instructions. Where the some power. See also power swap asset class is considered more important than the selection within that class, program

33 Equity Derivatives Glossary

P/Q trading (also known as basket trading) is PUTTABLE SWAP used to lower trading costs since trading a An interest rate swap in which the fixed-rate basket of shares is cheaper than buying or receiver has the right to terminate the selling those shares individually. Program contract after a specified period. The puttable trading is different from stock index swap is the opposite of a callable swap. The arbitrage, although it is used in such a fixed-rate payer is effectively sold a swaption, strategy. who receives a lower fixed rate in compensation. Puttable swaps are similar to PROMPT extendible swaps. Also known as a cancellable swap. For immediate (ie, two days) delivery.

PROTECTION LEVEL This refers to the safety level of the Q underlying at which the investor can still keep their capital intact. Once this level is breached, the original investment amount Q is at risk. UANTO PRODUCT An asset or liability denominated in a PUT OPTION currency other than that in which it is usually traded, typically equity index futures, equity See option index options, bond options and interest rate swaps (differential swaps). Quanto products Put spread can be hedged with an offsetting position in a A put spread reduces the cost of buying a local currency product. Variable asset and put option by selling another put at a lower foreign exchange exposures will arise with level. This limits the amount the purchaser changes in the foreign exchange rate and in can gain if the underlying goes down, but the underlying, so the structures must be the premium received from selling an out- continually dynamically hedged in a similar of-the money put partly finances the at- fashion to option products. See also the-money put. A put spread may also be guaranteed exchange rate option, joint option useful if the purchaser thinks there is only limited downside in the market. See also Q call spread, option combination strategies UANTO SWAP Also called a differential swap. A quanto PUT-CALL PARITY swap is a fixed-floating or floating-floating interest rate swap. One of the floating rates is The relationship between a European- a foreign interest rate, but is applied to a style put option and a European-style call notional amount denominated in the domestic option on the same underlying with the currency. For example, a US investor may same exercise price and maturity. Put-call enter into a five-year swap in which he makes parity states that the payout profile of a payments in US dollars at the six-month USD portfolio containing an asset plus a put Libor plus a spread semi-annually, and option is identical to that of a portfolio receives payments in US dollar at JPY Libor. containing a call option of the same strike The payments are calculated by applying the on that same asset (with the rest of the respective interest rates to a notional amount money earning the risk-free rate of return). of US$100 million. However, the notional In practice, a put option on, say, a stock principal can also be denominated in the index, can be constructed by shorting the Japanese yen, or in a third currency such as stock and buying a call option. The the British pound. A quanto swap enables the relationship means that traders are able to investor to avoid exchange rate risk while arbitrage mispriced options. See also taking advantage of interest rate differentials. reversal A corporate borrower with debt in a discount currency can use a quanto swap to lower his borrowing costs, while portfolio managers

34 Equity Derivatives Glossary

Q/R can use a quanto swap to enhance yield one in which the premium invested is rebated with higher interest rates in a discount if a designated boundary of the range is currency. breached first. A similar structure, the limit binary, is also essentially for trading. This is fundamentally a bet on a spot not staying within a predetermined range. The customer R specifies two spot rates, one above and one below the current spot rate. A premium is paid up front, and providing that both levels

trade (as monitored on a 24-hour basis), a fixed multiple of the premium invested will be Similar to a multi-factor option. It is an payable. See also trigger condition option with the payout linked to two or more underlying instruments or indexes. RANGE NOTE Some common types of rainbow options A range note (also known as a fairway note, are the maximum option, minimum option, an accrual note, or a corridor floater) is a best-of option and worst-of option. The structured note, which pays a coupon for underlyings are of the same asset class each day that the underlying spot stays within and can have different expiry dates and a specified range (sometimes called the strike prices, but for the option to payout, accrual corridor). If the underlying trades all the underlyings must move in the outside the specified range, the investor direction that is favourable to the option receives no interest for that day. The holder. However, if the option combines underlying can be a reference interest rate, a two or more types of asset classes, such foreign exchange rate, an equity price or the as a stock index and an exchange rate, it spread between two interest rates. The range is called a hybrid option. is determined at the outset to suit the

investor’s risk/return requirements, but might RANDOM WALK also be reset by the investor or be The series of values taken by a random automatically centred on the prevailing rate at variable with the progress of some each reset date. This higher yield is achieved parameter such as time. Each new value by the investor selling an embedded corridor (each new step in the walk) is selected option, particularly in times of high volatility. randomly and describes the path taken by The holder of the note will therefore benefit in the underlying variable. See also stable market periods when volatility is low. stochastic process RANGE RESETTABLE FORWARD RANGE ACCRUAL OPTION A type of forward contract that offers a more An option that pays out a fixed amount at favourable forward rate compared with an expiration for each day that the index rate ordinary forward, as long as the spot rate remains within the specified range. remains within a pre-defined range.

RANGE BINARY RATCHET FLOATER The range binary structure has been Also called a one-way floating rate note. A developed primarily for trading purposes ratchet floater is a structured note that pays a and is essentially a bet on a spot staying floating interest rate indexed on a reference within a given range. The strategy is often rate such as Libor. Each floating interest rate linked with a deposit for yield will depend on the previous interest rate paid. enhancement purposes. A range is specified by the customer over RATCHET OPTION a fixed period. A premium is paid up front See cliquet option and provided that the spot stays within the range (as monitored on a 24-hour basis), then a multiple of the premium invested will be payable. A rebate range binary is

35 Equity Derivatives Glossary

R

RATIO CALENDAR SPREAD For equities, this may be measured by a A strategy that involves the purchase of a stock’s beta, its standardised covariance with long-term option (either call or put) and the respect to the relevant equity index. See also selling of a greater amount of near-term specific risk option at the same strike price. REPLACEMENT COST REBATE Often used in terms of credit exposure, the Barrier options often have a rebate replacement cost of a financial instrument is associated with the trigger level(s). A its current value in the market – in other rebate is an amount paid to the holder of words, what it would cost to replace a given the derivative if the instrument is knocked- contract if the counterparty to the contract out or is never activated during its lifetime defaulted. Aside from bid-ask conventions, it as partial recompense for their initial is synonymous with market value. investment. One example is the rebate range binary. Regulatory arbitrage A REPLICATION financial transaction that allows one or To replicate the payout of an option by buying both of the counterparties to accomplish or selling other instruments. Creating a an operating or financial objective that synthetic option in this way is always possible would be unavailable to them directly in a complete market. In the case of dynamic because of regulations: for example, a replication this involves dynamically buying or commercial bank entering into a credit selling the underlying (or normally, because default swap with an OECD bank in order of cheaper transaction costs, futures) in to lower the regulatory capital that it must proportion to an option’s delta. In the case of hold. static replication the option (usually an exotic

option) is hedged with a basket of standard REGULATORY CAPITAL options whose composition does not change The amount of capital that an organisation with time – eg, an at-expiry digital option can is required to hold by its regulator. be replicated with a call spread. See also static replication, synthetic asset

REINVESTMENT RISK REPO AGREEMENT The risk that an asset manager will be unable to match the yield from an interest- To buy (sell) a security while at the same rate instrument (such as a swap or bond) time agreeing to sell (buy) the same security when reinvesting its coupon payments and at a predetermined future date. The price at principal repayments. which the reverse transaction takes place sets the interest rate over the period (the repo rate). The most active repo market is in R ELATIVE PERFORMANCE OPTION the US, where the Federal Reserve sets See outperformance option short-term interest rates by lending securities. In a reverse repo the buyer sells cash in RELATIVE PERFORMANCE RISK exchange for a security. Repos can benefit both parties. Buyers of repos often receive a The risk that a fund manager’s choice of better return than that available on equivalent investments will fail to match the money-market instruments; and financial performance of the benchmark against institutions, particularly dealers, are able to which the fund is measured, prompting get sub-Libor funding. A slight variation on fund redemptions. A similar risk is run by the repo is the buy/sell back. The buy/sell corporate treasury risk managers who are back’s coupon becomes the property of the measured against benchmark hedge purchaser for the duration of the agreement. levels. One way to address this type of risk It is preferred by credit-sensitive investors is with outperformance options. Relative such as central banks. performance risk is also used to refer to the risk that an individual asset will underperform relative to its asset class.

36 Equity Derivatives Glossary

R

REPO RATE constant maturity Treasuries) and increase if See repo agreement that index declines. The swap therefore exhibits positive convexity. Receiving fixed in a reverse index amortising swap (reverse R -IN-ARREARS SWAP ESET IAS) provides a hedge for instruments (such See delayed reset swap as mortgage swaps) that amortise as interest rates decline, although it is important to RESETTABLE CONVERTIBLE BOND ensure that the indexes on which the amortisation or accreting schedules are It is a convertible bond where the based are highly correlated. Unlike a conversion ratio can reset to a new value conventional IAS, the fixed receiver of a depending on the average price of the reverse IAS is buying volatility (sometimes underlying stock on pre-specified dates. referred to as ‘optionality’) which offsets the See also convertible bond short option position of a mortgage portfolio. See also mortgage swap REVERSAL To take advantage of mispriced options by REVERSIBLE SWAP creating a synthetic long futures position An interest rate swap in which one side has and edging it by selling futures contracts an option to alter the payment basis against it. A trader may buy an (fixed/floating) after a certain period. This is undervalued call, at the same time selling usually achieved by the use of a swaption, a fairly valued put and buying a futures allowing the purchaser the opportunity to contract. The same strategy could be enter a swap with payment on the opposite applied if the put was undervalued. The basis. The swaption would be for twice the ability to undertake this riskless arbitrage principal amount, one half nullifying the relies on put-call parity. See also original swap. convergence trade, put-call parity

RHO REVERSE BARRIER OPTION Measures an option’s sensitivity to a change See barrier option in interest rates. This will have an impact on both the future price of the option and the REVERSE CASH-AND-CARRY ARBITRAGE time value of the premium. Its impact A technique, used mainly in bond futures increases with the maturity of the option. and stock index futures, that involves buying a futures contract and selling the RISK NEUTRAL underlying. It is used when a futures An argument that underpins most derivatives contract is theoretically cheap, such as pricing, including the Black-Scholes model. when the implied repo rate is less than the The differential equation describing the price market repo rate. See also cash-and-carry of a derivative does not involve parameters arbitrage that depend on risk preferences. Derivatives prices in a market where all investors are risk REVERSE CONVERTIBLE neutral must therefore be the same as prices These are just like convertible bonds. The in the real world and this corollary main difference is that rather than buying a considerably simplifies model construction. call option on a stock, the investor sells a put on the stock or index. The investor RISK REVERSAL receives higher than normal coupons but The term ‘risk reversal’ is also used, by may lose some principal if the put ends up currency option traders, to denote the in the money. difference in implied volatility between out-of- the-money call and put options, which both REVERSE INDEX AMORTISING SWAP have a delta of 25%. The level of the risk An interest rate swap in which payments reversal is often used as a sentiment are linked to an index (eg, Libor or indicator in currency markets as it indicates

37 Equity Derivatives Glossary

R/S the relative demand for calls versus puts. above, the higher is paid. These swaps can See also collar, volatility skew be used to create asymmetric risk exposures, ie, cheaper fixed-rate funding for an oil ROLLER-COASTER SWAP producer when oil prices are low, or an enhanced yield for an insurance company An interest rate swap in which one when equity prices are falling. counterparty alternates between paying fixed and paying floating. Another name for a seasonal swap. SETTLEMENT RISK Settlement risk (delivery risk), as a particular ROLL-OVER RISK form of counterparty credit risk, arises from a non-simultaneous exchange of payments. The risk that a derivatives hedge position For example, a bank that makes a payment will be at a loss at expiry, necessitating a to a counterparty, but will not be cash payment when the expiring hedge is recompensed until a later date, is exposed to replaced with a new one. Normally, such a the risk that the counterparty may default roll-over loss simply represents an before making the counter-payment. opportunity loss, but sometimes the cash Settlement risk is distinct from market risk cost is consequential. because it relates to exposure to a counterparty rather than exposure to the underlying risk related to the reference entity of the derivatives contract. S SHOUT OPTION

A type of path-dependent option that allows SEASONAL SWAP the investor to lock in profits if he thinks the An interest rate swap in which the principal market has reached a high (for a call) or low alternates between zero and the notional (for a put). The investor benefits further if the amount (which can change or stay market finishes higher or lower than the shout constant). The principal amount of the level. The shout option is designed for swap is designed to hedge the seasonal investors who have a directional view on the borrowing needs of a company. market and want to take positions, but are worried about the volatility of the asset and want to lock in a minimum return. See also SECURITISATION lookback option, path-dependent option The conversion of assets (usually forms of debt) into securities, which can be traded SKEW more freely and cheaply than the underlying assets and generate better A skewed distribution is one that is returns than if the assets were used as asymmetric. Skew is a measure of this collateral for a loan. One example is the asymmetry. A perfectly symmetrical mortgage-backed security, which pools distribution has zero skew, whereas a illiquid individual mortgages into a single distribution with positive (negative) skew is tradable asset. one where outliers above (below) the mean are more probable. An example of an asymmetric distribution in the financial SEMI-FIXED SWAP markets is the distribution implied by the An interest rate swap with two possible presence of a volatility skew between out-of- fixed rates, which can be tailored to suit the-money call and put options. bullish or bearish market views. The rate paid by the fixed-rate payer depends on SPECIFIC RISK whether current Libor (or another reference rate or asset) is above or below Specific risk, also known as non-systematic a predetermined level. In a typical risk, represents the price variability of a structure, if Libor is below the trigger level, security that is due to factors unique to that the lower of the two rates is paid, if it is security, as opposed to that portion that is

38 Equity Derivatives Glossary

S due to systematic risk, the generalised hedge options, a static replication portfolio is price variability of the related interest rate a better hedge for gamma and volatility, as or equity market. As an example, a US well as delta, than dynamic replication. Static Treasury note would have no specific risk, replication can be used for hedging a position as it is deemed to have no risk other than in exotic options with vanilla options, or for movement in interest rates, while a replicating a long-term option with short-term would have a degree of options. In practice, however, it is not always default risk as well as more generalised possible to hedge using static replication. The yield curve risk. See also relative number of different options and notional performance risk amounts required can quickly become unmanageable. See also delta-hedging, SPREAD OPTION replication, synthetic asset

The underlying for a spread option is the price differential between two assets (a difference option) or the same asset at In the mid-1980s it was discovered that different times or places. An example of a exhibit autocorrelations – implying that earlier financial difference option is the credit price changes could be used to forecast spread option, the underlying for which is future changes. Statistical arbitrageurs seek the spread between two debt issues, to exploit these patterns in their trading which derives from the relative credit strategies. rating of the issuers. Another is the cross- currency cap, where the underlying is the STEP-DOWN SWAP spread between interest rates in two different currencies. A calendar spread, a The opposite of an escalating rate swap; ie, pair of options with the same strike price the fixed rate decreases in increments over but different maturities, pays out the price the life of the swap difference for a single asset on two different dates. Spread options, including STEP-UP SWAP calendar spreads, are particularly popular See accreting in the commodity markets.

STEP-UP/DOWN RANGE FORWARD SPREAD-LOCK SWAP A self-adjusting range forward structure, An interest rate swap in which one which is particularly suitable for hedging payment stream is referenced at a fixed purposes. If the strike level of the long put spread over a benchmark rate such as US option is breached, the strike automatically Treasuries. adjusts up or down (according to exposure) to a new, more favourable, level. Stochastic SQUEEZE optimisation model A model or description of Pressure on a particular delivery date a system in which the choice of action that resulting in making the price of that date can be taken is dependent on the values of higher relative to other delivery dates. some random variables. For example, the value of an American-style option is such that the best choice of exercise is always made. STATIC REPLICATION Static replication is a method of hedging STOCHASTIC PROCESS an options position with a position in standard options whose composition does Formally, a process that can be described by not change through time. The method the evolution of some random variable over attempts to replicate the payout of the some parameter, which may be either instrument in a more manageable fashion discrete or continuous. Geometric Brownian than dynamic replication, where a position motion is an example of a stochastic process in the underlying or futures contracts must parameterised by time. Stochastic processes be dynamically adjusted if it is to remain are used in finance to develop models of the effective. Because it uses options to future price of an instrument in terms of the

39 Equity Derivatives Glossary

S spot price and some random variable; or the futures and underlying prices diverge, it is analogously, the future value of an interest not worthwhile arbitraging the two. This or foreign exchange rate. See also arises as a result of transaction costs from Geometric Brownian motion, martingale, bid-ask spreads, the market impact of buying random walk and selling stock, and execution risks.

STOCHASTIC VOLATILITY STOCK INDEX OPTION One of the key assumptions of the Black- An option, either exchange-traded or over- Scholes model is that the stock price the-counter, on a stock index. follows geometric Brownian motion with constant volatility and interest rates. STOCK OPTION However, in real markets, volatility is far from constant. If volatility is assumed to be An option, either exchange-traded or over- driven by some stochastic process, the-counter, on an individual equity. however, the Black-Scholes model no longer describes a complete market, since STRADDLE there is now another source of uncertainty The sale or purchase of a put option and a in the option pricing model. A variety of call option, with the same strike price, on the approaches have been attempted to same underlying and with the same expiry. resolve this difficulty since the mid-1980s, The strike is normally set at-the-money. The most notably the Heath-Jarrow-Morton purchaser benefits, in return for paying two framework. premiums, if the underlying moves enough either way. It is a way of taking advantage of STOCK INDEX ARBITRAGE an expected upturn in volatility. Sellers of The technique of selling a futures contract straddles assume unlimited risk but benefit if on a stock index and buying the underlying the underlying does not move. Straddles are stocks, via programme trading, or vice primarily trading instruments. See also option versa when the price of the futures combination strategies contract is above or below its theoretical value. The ability to conduct such STRANGLE strategies depends on the efficiency of the 1.As with a straddle, the sale or purchase of futures and cash markets. a put option and a call option on the same instrument, with the same expiry, but at strike STOCK INDEX FUTURE prices that are out-of-the-money. The A futures contract on a stock index. Most strangle costs less than the straddle because are cash-settled. The theoretical price of a both options are out-of-the-money, but profits stock index future equals the cost of are only generated if the underlying moves carrying the underlying stock for that dramatically, and the break-even is worse period: the opportunity cost of the funds than for a straddle. Sellers of strangles make invested minus any dividends. If the cost money in the range between the two strike of buying and holding the underlying prices, but lose if the price moves outside the stocks is less than the futures price, an break-even range (the strike prices plus the arbitrageur can sell futures and buy the premium received). underlying stocks. 2.The term strangle is also used, by currency The higher interest rates are (compared option traders, to denote the average with the dividend yield), the greater the difference in implied volatility between out-of- opportunity cost of holding the stocks, the-money call and put options with a 25% hence the futures price should be higher delta and the implied volatility of at-the- than the current index price. If interest money forward options. See also option rates are less than the dividend yield, the combination strategies opportunity cost of holding stocks is less and the futures price should fall below the current index price. There is usually a so- called arbitrage band in which, although

40 Equity Derivatives Glossary

S

STRAP SUBSTITUTION OPTION A strategy that involves purchasing one A bilateral financial contract in which one put option and two call options, all with the party buys the right to substitute a specified exact same strike price, underlyings and asset or one of a specified group of assets for maturity date. another asset at a point in time or contingent upon a STRATEGIC ASSET ALLOCATION credit event.

The distribution of investment funds in response to long-term, fundamental SWAP expectations for markets. See accreting, credit default swap, delayed reset swap, digital swap, dual currency swap, STRESS-TESTING equity (index) swap, forward swap, high- coupon swap, index amortising swap, interest To perform a stress test on a derivatives rate swap, mortgage swap, municipal swap, position is to stimulate an extreme market participating swap, periodic resetting swap, event and examine its behaviour under the power swap, puttable swap, reverse index ‘stress’ of that event. amortising swap, reversible swap, roller- coaster swap, seasonal swap, semi-fixed STRIP swap, spread-lock swap, step-down swap, A strategy that involves the purchase of variable notional swap, yield curve swap, one call option and two put options, all with the same strike price on the same underlying and the same expiry date. The SWAPTION strikes are set at-the-money. Alternatively, An option to enter an interest rate swap. A a strip can refer to the process of payer swaption gives the purchaser the right removing coupons from a bond and selling to pay fixed, a receiver swaption gives the the stripped bond (or zero coupon bond) purchaser the right to receive fixed (pay and interest-paying coupons separately. floating). Apart from those in the sterling market, many STRUCTURED PRODUCT swaptions are capital-market driven. Good- A structured product is an investment that quality borrowers are able to issue puttable or bundles up a portfolio of securities and callable bonds and use the swaptions market other derivatives to create a single to reduce their financing costs. In the case of product. For example, a structured note callable bonds, the issuer effectively buys an can be a five-year bond that has an option from the investor in return for a slightly embedded equity or currency option in higher coupon, so that it may benefit if rates order to enhance its return. A structured decline. Because many of these embedded product appeals to the investor who has a options have traditionally been underpriced, view on the market and a good idea of good-quality borrowers have been able to what his risk/reward appetite is. monetise this anomaly by selling an equivalent swaption (a receiver swaption) to a bank at market rates. STRUCTURED YIELD INVESTMENTS The profit from this arbitrage lowers funding Any security (normally a structured note) costs. If the swaption is exercised against the whose yield is conditional on certain issuer, it calls the bonds (although the issuer trigger conditions being met. Such a would almost certainly have called the issue security is normally constructed by given the reduction in rates). In the case of embedding path-dependent options (such puttable bonds, the borrower sells a swaption as binary options) in a vanilla debt issue. to the swaption market. The premium gained The investor’s return on the note will then lowers the funding cost at the expense of vary according to the payout of the leaving the borrower unsure of the maturity of options. the debt.

41 Equity Derivatives Glossary

S/T

SYNTHETIC ASSET SYNTHETIC SECURITISATION A synthetic asset is a combination of long A first-loss basket swap structure that and short positions in financial references a portfolio of bonds, loans or other instruments, which has the same financial instruments held on a firm’s balance risk/reward profile as another instrument. sheet. The technique replicates the credit risk For example, it is possible to replicate the transfer benefits of a traditional cash payout and exposure of a short futures securitisation while retaining the assets on position by going short European-style call balance sheet. Advantages over cash options and long European puts with securitisation include reduced cost, ease of identical strikes and expiries. Synthetic execution and retention of on-balance sheet index options can be generated either funding advantage. through positions in the underlying and futures contracts, or with a basket of SYSTEMIC RISK vanilla options. See also replication, static replication The risk that the financial system as a whole may not withstand the effects of a market crisis. Concern on the part of banking SYNTHETIC COLLATERALISED DEBT regulators has been caused by the OBLIGATION concentration of derivative risk among a A synthetic collateralised debt obligation relatively small number of market (CDO) uses credit derivatives to transfer participants, with the concomitant risk that the credit risk in a portfolio. This is in contrast failure of a major dealer could have serious to a traditional CDO, which is typically knock-on effects for many other market structured as a securitisation with participants. ownership of the assets transferred to a separate special purpose vehicle (SPV). The assets are funded with the proceeds of debt and equity issued by the vehicle. In T a synthetic CDO, an institution transfers the total return or default risk of a reference portfolio via a credit default swap, a , or a credit- TABLE TOP linked note. The SPV then issues Similar to a , except that the securities with repayment contingent upon purchase of an option is financed by sales of the loss on the portfolio. Proceeds are the same option at two different strike prices. either held by the vehicle and invested in highly rated, liquid collateral, or passed-on TACTICAL ASSET ALLOCATION to the institution as an investment in a credit-linked note. Balance sheet synthetic The distribution of investment funds in CDOs are typically used by banks to response to short-term expectations of manage risk capital and are easier to market opportunity or threat. execute than traditional CDOs. Arbitrage synthetic CDOs are often used by THETA insurance companies and asset managers and exploit the spread between the yield This measures the effect on an option’s price on the underlying assets and the reduced of a one-day decrease in the time to expense of servicing a CDO structure. See expiration. The more the market and strike also collateralised debt obligation prices diverge, the less effect theta has on a vanilla option’s price. Theta is also non-linear for vanilla options, meaning that its value SYNTHETIC FORWARD decreases faster as the option is closer to See synthetic asset maturity. Positive gamma is generally associated with negative theta and vice versa. SYNTHETIC OPTION

See synthetic asset, replication

42 Equity Derivatives Glossary

T

TIME DECAY tranche products, and the offer period is See theta usually four to eight weeks.

TIME VALUE TRANSLATION RISK The value of an option, other than its An accounting/financial reporting risk where intrinsic value. The time value therefore the earnings of a company can be adversely includes cost of carry and the probability affected due to its method of accounting for that the option will be exercised (which in foreign operations. turn depends on its volatility). TREASURY LOCK TOTAL RETURN SWAP A rate agreement based on the yield or A bilateral financial contract in which one equivalent market price of a reference US party (the total return payer) makes Treasury security. These can be settled floating payments to the other party (the based on yield differential for a full tenor, or total return receiver) equal to the total can be price-settled based on the exact return on a specified asset or index characteristics of a specific security. (including interest or dividend payments and net price appreciation) in exchange for TRIGGER amounts that generally equal the total Many path-dependent options have payouts return payer’s cost of holding the specified that depend on the underlying asset or index asset on its balance sheet. Price or coupons paid/payable reaching a specified appreciation or depreciation may be level before the expiry date. This level is the calculated and exchanged at maturity or trigger. Some options have more than one on an interim basis. A total (rate of ) return trigger level, in which case the payouts are swap is a form of credit derivative, but is conditional or increase with the number of distinct from a credit default swap in that triggers activated or the order in which they floating payments are based on the total are activated. See barrier option, Parisian economic performance of a specified barrier option asset and are not contingent upon the occurrence of a credit event. TRIGGER CONDITION TOTAL RETURN OPTION Path-dependent derivatives such as barrier options and binary options have payouts A total return option is a put option on which depend in some way on a market debt. An investor that has a risky variable satisfying a specific condition during corporate bond and is worried about the derivative’s life. If this ‘trigger condition’ is default can buy a total return option that met, the derivative may pay out immediately allows him to sell the bond at par if the (early exercise) or at some other specified corporation defaults. time (such as expiry). Alternatively, the option

may only become effective (be knocked-in) or TRACKING ERROR be de-activated (knocked out) when the Refers to the difference between the trigger condition is met. performance of a portfolio of stocks and a The most common condition is that the spot broad-based index with which they are rate or price of the underlying must breach a being compared. specified level, meaning that it must trade through the barrier, either from above or below. Many other trigger conditions are T RANCHE PRODUCT possible, however. Some examples include: A tranche product is one that is open for ¦¦the spot must breach the trigger, and remain subscription for only a limited period, as above/below it for a specified time; opposed to open-ended products, which ¦¦the spot trades at the trigger level at a accept investments for an unlimited specified time (eg, expiry) or at any time period. Most structured products are during the option’s life;

43 Equity Derivatives Glossary

T/U

¦¦the spot trades within or breaks out of a or interest rate levels and curve steepness (a range (for example, range binaries); stochastic interest rate model). Two-factor ¦¦there is more than one trigger level, with models model interest rate curve movements the payout conditional upon or increasing more realistically than one-factor models. with the number of triggers activated and possibly the order in which they are TWO-NAME EXPOSURE activated (for example, a mini-premium option); Credit exposure that the protection buyer has ¦¦some combination of these. to the protection seller, which is contingent on See also barrier option, Parisian barrier the performance of the reference credit. If the option, range binary protection seller defaults, the buyer must find alternative protection and will be exposed to changes in replacement cost due to changes TRIGGER FORWARD in credit spreads since the inception of the The trigger forward is primarily designed original swap. More seriously, if the for trading purposes, although it can also protection seller defaults and the reference be used as an alternative hedge. It is entity defaults, the buyer is unlikely to recover usually a zero-cost structure, whereby the the full default payment due, although the purchaser enters into an outright forward final recovery rate on the position will benefit transaction at a rate significantly more from any positive recovery rate on obligations attractive than the prevailing market rate, of both the reference entity and the protection but where the whole structure will be seller. knocked out if a predetermined trigger level is reached at any time before the expiry date. U Similar to a binomial tree, a trinomial tree is a discrete-time model describing the UNDERLYING distribution of assets. After each time step The underlying of a structured product or in the trinomial tree there are three option can be any asset class (equity index, possible outcomes; an up move, a down stock basket, debt instrument, interest rate, move or no move in the asset value. This commodity or a combination of these) that is gives additional degrees of freedom, which used to construct the product and whose enhance the computational power of the performance is a key determinant of the . payout. In some products, the underlying may

be a basket of 20 stocks, but the redemption TURBO basket that is used to calculate the maturity A type of path-dependent option, usually payout may comprise only 10 of those stocks. embedded in warrants. A barrier is set at the same level as the strike price, and if UNDERWATER the underlying ever touches the barrier at Has the same meaning as out-of-the-money. any point during the life of the turbo option, this will immediately cause the warrant to expire worthless. If the underlying never UP-AND-IN reaches the strike during the option’s life, A type of barrier option that pays off only the payout will be similar to a vanilla when the underlying index reaches the upper warrant. barrier during the life of the option.

TWO-FACTOR MODEL UP-AND-OUT Any model or description of a system that A type of barrier option that knocks out when assumes two sources of uncertainty or the underlying reaches the strike. variables; for example, an asset price and its volatility (a model),

44 Equity Derivatives Glossary

V

to profit from this correlation. See also vega V VARIABLE NOTIONAL OPTION/SWAP An option or swap where the notional value is VALUE-AT-RISK linked to the underlying asset price or rate. Usually changes in the notional will be Formally, the probabilistic bound of market directly proportional to changes in the losses over a given period of time (known underlying price; ie, they both decrease or as the holding period) expressed in terms increase together. Such derivatives have two of a specified degree of certainty (the main uses. In an , the fixed-rate confidence interval). Put more simply, the receiver can opt to receive the return of either value-at-risk (VaR) is the worst-case loss a fixed number of stocks, or the number of expected over the holding period within stocks that could be purchased for a fixed the probability set out by the confidence sum. The former case amounts to a variable interval. Larger losses are possible, but notional amount for the swap. An example with a low probability. For instance, a using an option is the case of a firm that sells portfolio whose VaR is $20 million over a more exports as exchange rates decline and one-day holding period, with a 95% its products therefore become cheaper confidence interval, would have only a 5% abroad. Since it now has greater foreign chance of suffering an overnight loss currency revenue to hedge, it would purchase greater than $20 million. Calculation of a variable notional currency option for this VaR entails modelling the possible market purpose. moves over the holding period, incorporating correlations among market factors, calculating the impact of such VARIANCE GAMMA MODEL potential market moves on portfolio A jump model that better captures the positions, and combining the results to characteristics of the volatility smile for examine risk at different levels of shorter-dated options than stochastic volatility aggregation. The three main approaches models. to this analysis are historical simulation, the analytical approach using a correlation V matrix or empirical (Monte Carlo) ARIANCE SWAP simulation. Major trading houses expend The cash payout of a is equal considerable energies on their VaR to notional multiplied by the difference methodologies and have lobbied between the realised variance of the regulators to recognise their efforts, with underlying index over the life of the swap and some success. the strike variance.

VANILLA OPTION VASICEK MODEL Also known as a plain vanilla option. A An interest rate model that incorporates vanilla option is a standard call or put mean reversion and a constant volatility for option in its most basic form. the short interest rate. It is a one-factor model from which discount bond prices and options on those bonds can be deduced. All have VANNA closed-form solutions. The vega of an option is not constant. Vega changes as spot changes and as V volatility changes. The vanna of an option EGA measures the change in vega for a change Measures the change in an option’s price in the underlying spot. caused by changes in volatility. Vega is at its As spot moves deeper out-of-the-money highest when an option is at-the-money. It for a vanilla option the vega is lower. If decreases the more the market and strike spot and volatility movements are prices diverge. Options closer to expiration positively correlated the holder of an have a lower vega than those with more time option with positive vanna will be expected to run. Positions with positive vega will

45 Equity Derivatives Glossary

V generally have positive gamma. To be and demand and supply. See also implied long vega (to have a positive vega) is volatility, risk reversal achieved by purchasing either put or call options. Positions that are long vega VOLATILITY SMILE benefit from increases in implied volatility but also from actual volatility if the option A graph of the implied volatility of an option is being delta hedged. They will also lose versus its strike (for a given tenor) typically from reductions in volatility. Spread describes a smile-shaped curve – hence the options can be an exception: a reduction term ‘volatility smile’. This can be attributed to in the volatility of one of the assets may the belief that the underlying distribution is actually increase the price of the option leptokurtic, since this tends to increase the because the correlation between the two value of out-of-the-money options. assets decreases. Vega is sometimes known as kappa or tau. See also gamma, vanna, vomma The cash payout of a volatility swap is equal to notional multiplied by the difference between the realised volatility of the Any option strategy that relies on the underlying index over the life of the swap and difference in premium between two the strike volatility. options on the same underlying with the same maturity, but different strike prices. VOLATILITY TERM STRUCTURE Thus put spreads and call spreads would The term structure of volatility is the curve both be vertical spreads. Volatility A depicting the differing implied volatilities of measure of the variability (but not the options with differing maturities. Such a curve direction) of the price of the underlying arises partly because implied volatility in instrument. It is defined as the annualised short options changes much faster than for standard deviation of the natural log of the longer options. However, the volatility term ratio of two successive prices. Historical structure also arises because of assumed volatility is a measure of the standard mean reversion of volatility. The effect of deviation of the underlying instrument over changes in volatility on the option price is less a past period. Implied volatility is the the shorter the option. Most market-makers volatility implied in the price of an option. take advantage of differing volatilities to All things being equal, higher volatility will hedge their books or to trade perceived lead to higher vanilla option prices. In anomalies in volatility. Such strategies have traditional Black-Scholes models, volatility to be weighted because of the differing vega is assumed to be constant over the life of effects. See also implied volatility an option. Since traders mainly trade volatility, this is clearly unrealistic. New techniques have been developed to cope VOLATILITY TRADING with volatility’s variability. The best known A strategy based on a view that future are stochastic volatility, Arch and Garch. volatility in the underlying will be more or less than the implied volatility in the option price. VOLATILITY SKEW Option market-makers are volatility traders. The most common way to buy/sell volatility is The difference in implied volatility between to buy/sell options, hedging the directional out-of-the-money puts and calls. In most risk with the underlying. Volatility buyers equity option markets out-of-the money make money if the underlying is more volatile calls have lower implied volatility than out- than the implied volatility predicted. Sellers of of-the-money puts. This is mostly ascribed volatility benefit if the opposite holds. Other to the greater supply of volatility above, methods of buying/selling volatility are to rather than below, the money since fund buy/sell combinations of options, the most managers are happy to write calls and not usual being to buy/sell straddles or strangles. so happy to write puts. Volatility skews can Other strategies take advantage of the be very pronounced in the currency difference between implied volatilities of markets although whether puts or calls are differing maturity options, not between favoured depends on market sentiment

46 Equity Derivatives Glossary

V/W implied and actual volatility. For example, if implied volatility in short-term options is WEDDING CAKE DEPOSIT high and in longer options low, a trader can sell short-term options and buy longer A type of range deposit where there is an ones. inner range and one or more outer ranges. The payout from the product is at its maximum when the underlying remains in the VOMMA inner range, and this is reduced successively The vega of an option is not constant. when the spot reaches each outer range. Vega changes as spot changes and as This product is suitable for investors who volatility changes. The vomma of an option have a range-bound view, and want to take is defined as the change in vega for a less risk. change in volatility. Vomma measures the convexity of an option price with respect to WEEKLY RESET FORWARD volatility. Vega is to vomma (volatility gamma) as delta is to gamma for spot A weekly reset forward is a synthetic forward movements. Holders of options with a high where a portion of the contract is locked in vomma benefit from volatility of volatility. each week, provided that the spot rate that See also vega week meets a predetermined fixing criterion. Hence the purchaser can deal at a rate better than the forward outright, but only in an amount corresponding to the frequency with which the criterion has been met. If the W criterion is met in none of the weeks during the life of the contract, then the contract is not activated at WARRANT all; if it is met every week, the overall rate is favourable compared with the initial prevailing An instrument giving the purchaser the market rate. The weekly reset forward is used right, but not the obligation, to purchase or for those with cash-flows spread over time or sell a specified amount of an asset at a to hedge balance sheets. certain price over a specified period of time. Warrants differ from options only in that they are usually listed. Underlying WINDOW BARRIER assets include equity, debt, currencies and A window barrier is a type of barrier option for commodities. See also equity warrant which the barrier strike only applies for a specified period during the option’s life. If the WASTING ASSET spot breaches this level during the window period, then the option either knocks in or A wasting asset is a derivative security knocks out. If the option is not activated that loses value due to time decay and during the window period, the option will which may expire worthless at maturity. retain the features of a vanilla option and Derivatives such as options, rights and expire at maturity. warrants are considered to be wasting assets. WORST-OF OPTION An option whose payout is referenced to one or more of the worst performers in a basket of Typically swaps and vanilla options such shares or indexes. as calls, puts, caps, floors and collars with payouts linked to temperature, precipitation, humidity or windspeed. Most instruments are linked to heating degree days or cooling degree days. These two indexes measure the deviation of the average of a day’s high and low temperature from a baseline reference temperature.

47 Equity Derivatives Glossary

Y/Z

taking a view on a bond market’s direction. It Y is normally structured as the yield of a longer maturity bond minus the yield of a shorter one. A call would therefore appreciate in value as a

curve flattened. A put would decrease in YIELD value. Such options were developed in the US The interest rate that will make the present in 1991 in response to a steepening yield value of the cashflows from an investment curve. equal to the price (or cost) of the investment. Also called the internal rate of YIELD CURVE SWAP return. The relates the annual A swap in which the two interest streams coupon yield to the market price by dividing reflect different points on the swap yield curve. the coupon by the price divided by 100 and Yield curve swaps can be used to exploit a ignores the time value of money or yield curve steepening or flattening view. For potential capital gains or losses. Simple example, one side pays the two-year Constant takes into account the Maturity Treasury (CMT) rate and the other effect of the capital gain or loss on maturity the 10-year CMT rate. of a bond in addition to the current yield.

YIELD ADJUSTMENT A payment by one counterparty, usually at Z the outset of a swap or at a reset date, to compensate the other counterparty for entering into a swap on off-market terms. Z ERO COST COLLAR YIELD CURVE See zero cost option

The yield curve is a graphical Z representation of the term structure of ERO COST OPTION interest rates. It is usually depicted as the Any option strategy that involves financing an spot yields on bonds with different option purchase by the simultaneous sale of maturities but the same risk factors (such another option so that paid and received as creditworthiness of issuer), plotted premiums exactly offset one another. See also against maturity. The usual features of a collar, participating forward Zero coupon bond spot yield curve are higher long-term yields A debt instrument issued at below . than short-term yields and a curve for The bond pays no coupons; instead, it is default-free bonds that is lower at each redeemed at face value at maturity. point than the equivalent curve for riskier debt. It is possible to construct variants of ZERO COUPON SWAP the yield curve from this basic form. The par yield curve is found by calculating the An off-market swap in which either or both of coupons that would be necessary for bonds the counterparties makes one payment at of each maturity to be priced at maturity. Usually it is the fixed-rate payments par; the forward yield curve is found by only that are deferred. The party not receiving extrapolating the spot yield curve point-by- payment until maturity incurs a greater credit point, based on the implied forward interest risk than it would with an ordinary swap. The rates. swap is advantageous for a company that will not receive payment for a project until it is completed or to hedge zero coupon liabilities, YIELD CURVE AGREEMENT such as zero coupon bonds. See yield curve swap ZERO EXERCISE PRICE OPTION (ZEPO) YIELD CURVE OPTION A low exercise price option whose strike price An option that allows investors to take a is exactly zero. view on the shape of a yield curve without

48 Equity Derivatives Glossary

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