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Introduction to Forwards and Futures Introduction to Forwards and Futures Liuren Wu Zicklin School of Business, Baruch College Options Markets Liuren Wu (Baruch) Forwards & Futures Options Markets 1 / 38 Outline 1 Derivatives 2 Forwards 3 Futures 4 Forward pricing 5 Interest rate parity 6 Hedging using Futures Liuren Wu (Baruch) Forwards & Futures Options Markets 2 / 38 Derivatives Derivatives are financial instruments whose returns are derived from those of another (\underlying") financial instrument. Cash markets or spot markets I The sale is made, the payment is remitted, and the good or security is delivered immediately or shortly thereafter. Derivative markets I Derivative markets are markets for contractual instruments whose performance depends on the performance of another instrument, the so called underlying. Liuren Wu (Baruch) Forwards & Futures Options Markets 3 / 38 Derivatives Markets Exchange-traded instruments (Listed products) I Exchange traded securities are generally standardized in terms of maturity, underlying notional, settlement procedures ... I By the commitment of some market participants to act as market-maker, exchange traded securities are usually very liquid. F Market makers are particularly needed in illiquid markets. I Many exchange traded derivatives require "margining" to limit counterparty risk. I On some (most) exchanges, the counterparty is the exchange itself, or a central clearing house, yielding the advantage of anonymity. Liuren Wu (Baruch) Forwards & Futures Options Markets 4 / 38 Derivatives Markets Over-the-counter market (OTC) I OTC securities are not listed or traded on an organized exchange. I An OTC contract is a private transaction between two parties (counterparty risk). I A typical deal in the OTC market is conducted through a telephone or other means of private communication. I The terms of an OTC contract are usually negotiated on the basis of an ISDA master agreement (International Swaps and Derivatives Association). I The distinction between OTC and exchange-listed may become smaller over time: F Some also calls Nasdaq market as OTC. F In an effort to eliminate/alleviate counterparty risk, regulations are pushing some OTC contracts to central clearing. Liuren Wu (Baruch) Forwards & Futures Options Markets 5 / 38 Derivatives Products Forwards (OTC) Futures (exchange listed) Swaps (OTC) Options (both OTC and exchange listed) Liuren Wu (Baruch) Forwards & Futures Options Markets 6 / 38 Derivative Traders Hedgers Speculators Arbitrageurs Comments: Some of the largest trading losses in derivatives have occurred because individuals who had a mandate to be hedgers or arbitrageurs switched to being speculators. Hedging activities by themselves can also lead to big losses...at least indirectly. When hedging fails, many attack the efficiency of the hedging model, but many times the large loss comes from the fact that the hedging model is very efficient most of the time... Liuren Wu (Baruch) Forwards & Futures Options Markets 7 / 38 Review: Valuation and investment in primary securities The securities have direct claims to future cash flows. Valuation is based on forecasts of future cash flows and risk: I DCF (Discounted Cash Flow Method): Discount forecasted future cash flow with a discount rate that is commensurate with the forecasted risk. Investment: Buy if market price is lower than model value; sell otherwise. Both valuation and investment depend crucially on forecasts of future cash flows (growth rates) and risks (beta, credit risk). Liuren Wu (Baruch) Forwards & Futures Options Markets 8 / 38 Compare: Derivative securities Payoffs are linked directly to the price of an \underlying" security. Valuation is mostly based on replication/hedging arguments. I Find a portfolio that includes the underlying security, and possibly other related derivatives, to replicate the payoff of the target derivative security, or to hedge away the risk in the derivative payoff. I Since the hedged portfolio is riskfree, the payoff of the portfolio can be discounted by the riskfree rate. I Models of this type are called \no-arbitrage" models. Key: No forecasts are involved. Valuation is based on cross-sectional comparison. I It is not about whether the underlying security price will go up or down (given growth rate or risk forecasts), but about the relative pricing relation between the underlying and the derivatives under all possible scenarios. Liuren Wu (Baruch) Forwards & Futures Options Markets 9 / 38 Arbitrage in a Micky Mouse Model The current prices of asset 1 and asset 2 are 95 and 43, respectively. Tomorrow, one of two states will come true I A good state where the prices go up or I A bad state where the prices go down Asset1 = 100 Asset2 = 50 Asset1 = 95 P Asset2 = 43 PPP Asset1 = 80 Asset2 = 40 Do you see any possibility to make risk-free money out of this situation? Liuren Wu (Baruch) Forwards & Futures Options Markets 10 / 38 DCF versus No-arbitrage pricing in the Micky Mouse Model DCF: Both assets could be over-valued or under-valued, depending on our estimates/forecasts of the probability of the good/bad states, and the discount rate. No-arbitrage model: The payoff of asset 1 is is twice as much as the payoff of asset 2 in all states, then the price of asset 1 should be twice as much as the price of asset 2. I The price of asset 1 is too high relative to to the price of asset 2. I The price of asset 2 is too low relative to to the price of asset 1. I I do not care whether both prices are too high or low given forecasted cash flows. I Sell asset 1 and buy asset 2, you are guaranteed to make money | arbitrage. I Selling asset 1 alone or buying asset 2 alone is not enough. Again: DCF focuses on time-series forecasts (of future). No-arbitrage model focuses on cross-sectional comparison (no forecasts)! Can you think of a case when the arbitrage trading can blow up, even if all assumptions are true? Liuren Wu (Baruch) Forwards & Futures Options Markets 11 / 38 Forward contracts: Definition A forward contract is an OTC agreement between two parties to exchange an underlying asset I for an agreed upon price (the forward price) I at a given point in time in the future (the expiry date) Example: On June 3, 2003, Party A signs a forward contract with Party B to sell 1 million British pound (GBP) at 1.61 USD per 1 GBP six month later. I Today (June 3, 2003), sign a contract, shake hands. No money changes hands. I December 6, 2003 (the expiry date), Party A pays 1 million GBP to Party B, and receives 1.61 million USD from Party B in return. I Currently (June 3), the spot price for the pound (the spot exchange rate) is 1.6285. Six month later (December 3), the exchange rate can be anything (unknown). I 1.61 is the forward price. Liuren Wu (Baruch) Forwards & Futures Options Markets 12 / 38 Foreign exchange quotes for GBPUSD June 3, 2003 Maturity bid offer spot 1.6281 1.6285 1-month forward 1.6248 1.6253 3-month forward 1.6187 1.6192 6-month forward 1.6094 1.6100 The forward prices are different at different maturities. I Maturity or time-to-maturity refers to the length of time between now and expiry date (1m, 2m, 3m etc). I Expiry (date) refers to the date on which the contract expires. I Notation: Forward price F (t; T ): t: today, T : expiry, τ = T − t: time to maturity. I The spot price S(t) = F (t; t). [or St ; Ft (T )] Forward contracts are the most popular in currency and interest rate markets. Liuren Wu (Baruch) Forwards & Futures Options Markets 13 / 38 Forward price revisited The forward price for a contract is the delivery price (K) that would be applicable to the contract if were negotiated today. It is the delivery price that would make the contract worth exactly zero. I Example: Party A agrees to sell to Party B 1 million GBP at the price of 1.3USD per GBP six month later, but with an upfront payment of 0.3 million USD from B to A. I 1.3 is NOT the forward price. Why? I If today's forward price is 1.61, what's the value of the forward contract with a delivery price (K) of 1.3? The party that has agreed to buy has what is termed a long position. The party that has agreed to sell has what is termed a short position. I In the previous example, Party A entered a short position and Party B entered a long position on GBP. I But since it is on exchange rates, you can also say: Party A entered a long position and Party B entered a short position on USD. Liuren Wu (Baruch) Forwards & Futures Options Markets 14 / 38 Profit and Loss (P&L) in forward investments By signing a forward contract, one can lock in a price ex ante for buying or selling a security. Ex post, whether one gains or loses from signing the contract depends on the spot price at expiry. In the previous example, Party A agrees to sell 1 million pound at $1.61 per GBP at expiry. If the spot price is $1.31 at expiry, what's the P&L for party A? I On Dec 3, Party A can buy 1 million pound from the market at the spot price of $1.31 and sell it to Party B per forward contract agreement at $1.61. I The net P&L at expiry is the difference between the strike price (K = 1:61) and the spot price (ST = 1:31), multiplied by the notional (1 million). Hence, 0.3 million. If the spot rate is $1.71 on Dec 3, what will be the P&L for Party A? What's the P&L for Party B? Liuren Wu (Baruch) Forwards & Futures Options Markets 15 / 38 Profit and Loss (P&L) in forward investments (K = 1:61) long forward:( ST − K) short forward:( K − ST ) 0.5 0.5 0.4 0.4 T −K 0.3 0.3 T 0.2 0.2 0.1 0.1 0 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 P&L from long forward, S P&L from short forward, K−S −0.4 −0.4 −0.5 −0.5 1 1.2 1.4 1.6 1.8 2 1 1.2 1.4 1.6 1.8 2 Spot price at expiry, S Spot price at expiry, S T T Counterparty risk: There is a possibility that either side can default on the contract.
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