Term Structure Lattice Models
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Form Dated March 20, 2007 Swaption Template (Full Underlying Confirmation)
Form Dated March 20, 2007 Swaption template (Full Underlying Confirmation) CONFIRMATION DATE: [Date] TO: [Party B] Telephone No.: [number] Facsimile No.: [number] Attention: [name] FROM: [Party A] SUBJECT: Swaption on [CDX.NA.[IG/HY/XO].____] [specify sector, if any] [specify series, if any] [specify version, if any] REF NO: [Reference number] The purpose of this communication (this “Confirmation”) is to set forth the terms and conditions of the Swaption entered into on the Swaption Trade Date specified below (the “Swaption Transaction”) between [Party A] (“Party A”) and [counterparty’s name] (“Party B”). This Confirmation constitutes a “Confirmation” as referred to in the ISDA Master Agreement specified below. The definitions and provisions contained in the 2000 ISDA Definitions (the “2000 Definitions”) and the 2003 ISDA Credit Derivatives Definitions as supplemented by the May 2003 Supplement to the 2003 ISDA Credit Derivatives Definitions (together, the “Credit Derivatives Definitions”), each as published by the International Swaps and Derivatives Association, Inc. are incorporated into this Confirmation. In the event of any inconsistency between the 2000 Definitions or the Credit Derivatives Definitions and this Confirmation, this Confirmation will govern. In the event of any inconsistency between the 2000 Definitions and the Credit Derivatives Definitions, the Credit Derivatives Definitions will govern in the case of the terms of the Underlying Swap Transaction and the 2000 Definitions will govern in other cases. For the purposes of the 2000 Definitions, each reference therein to Buyer and to Seller shall be deemed to refer to “Swaption Buyer” and to “Swaption Seller”, respectively. This Confirmation supplements, forms a part of and is subject to the ISDA Master Agreement dated as of [ ], as amended and supplemented from time to time (the “Agreement”) between Party A and Party B. -
Up to EUR 3,500,000.00 7% Fixed Rate Bonds Due 6 April 2026 ISIN
Up to EUR 3,500,000.00 7% Fixed Rate Bonds due 6 April 2026 ISIN IT0005440976 Terms and Conditions Executed by EPizza S.p.A. 4126-6190-7500.7 This Terms and Conditions are dated 6 April 2021. EPizza S.p.A., a company limited by shares incorporated in Italy as a società per azioni, whose registered office is at Piazza Castello n. 19, 20123 Milan, Italy, enrolled with the companies’ register of Milan-Monza-Brianza- Lodi under No. and fiscal code No. 08950850969, VAT No. 08950850969 (the “Issuer”). *** The issue of up to EUR 3,500,000.00 (three million and five hundred thousand /00) 7% (seven per cent.) fixed rate bonds due 6 April 2026 (the “Bonds”) was authorised by the Board of Directors of the Issuer, by exercising the powers conferred to it by the Articles (as defined below), through a resolution passed on 26 March 2021. The Bonds shall be issued and held subject to and with the benefit of the provisions of this Terms and Conditions. All such provisions shall be binding on the Issuer, the Bondholders (and their successors in title) and all Persons claiming through or under them and shall endure for the benefit of the Bondholders (and their successors in title). The Bondholders (and their successors in title) are deemed to have notice of all the provisions of this Terms and Conditions and the Articles. Copies of each of the Articles and this Terms and Conditions are available for inspection during normal business hours at the registered office for the time being of the Issuer being, as at the date of this Terms and Conditions, at Piazza Castello n. -
Futures and Options Workbook
EEXAMININGXAMINING FUTURES AND OPTIONS TABLE OF 130 Grain Exchange Building 400 South 4th Street Minneapolis, MN 55415 www.mgex.com [email protected] 800.827.4746 612.321.7101 Fax: 612.339.1155 Acknowledgements We express our appreciation to those who generously gave their time and effort in reviewing this publication. MGEX members and member firm personnel DePaul University Professor Jin Choi Southern Illinois University Associate Professor Dwight R. Sanders National Futures Association (Glossary of Terms) INTRODUCTION: THE POWER OF CHOICE 2 SECTION I: HISTORY History of MGEX 3 SECTION II: THE FUTURES MARKET Futures Contracts 4 The Participants 4 Exchange Services 5 TEST Sections I & II 6 Answers Sections I & II 7 SECTION III: HEDGING AND THE BASIS The Basis 8 Short Hedge Example 9 Long Hedge Example 9 TEST Section III 10 Answers Section III 12 SECTION IV: THE POWER OF OPTIONS Definitions 13 Options and Futures Comparison Diagram 14 Option Prices 15 Intrinsic Value 15 Time Value 15 Time Value Cap Diagram 15 Options Classifications 16 Options Exercise 16 F CONTENTS Deltas 16 Examples 16 TEST Section IV 18 Answers Section IV 20 SECTION V: OPTIONS STRATEGIES Option Use and Price 21 Hedging with Options 22 TEST Section V 23 Answers Section V 24 CONCLUSION 25 GLOSSARY 26 THE POWER OF CHOICE How do commercial buyers and sellers of volatile commodities protect themselves from the ever-changing and unpredictable nature of today’s business climate? They use a practice called hedging. This time-tested practice has become a stan- dard in many industries. Hedging can be defined as taking offsetting positions in related markets. -
Finance: a Quantitative Introduction Chapter 9 Real Options Analysis
Investment opportunities as options The option to defer More real options Some extensions Finance: A Quantitative Introduction Chapter 9 Real Options Analysis Nico van der Wijst 1 Finance: A Quantitative Introduction c Cambridge University Press Investment opportunities as options The option to defer More real options Some extensions 1 Investment opportunities as options 2 The option to defer 3 More real options 4 Some extensions 2 Finance: A Quantitative Introduction c Cambridge University Press Investment opportunities as options Option analogy The option to defer Sources of option value More real options Limitations of option analogy Some extensions The essential economic characteristic of options is: the flexibility to exercise or not possibility to choose best alternative walk away from bad outcomes Stocks and bonds are passively held, no flexibility Investments in real assets also have flexibility, projects can be: delayed or speeded up made bigger or smaller abandoned early or extended beyond original life-time, etc. 3 Finance: A Quantitative Introduction c Cambridge University Press Investment opportunities as options Option analogy The option to defer Sources of option value More real options Limitations of option analogy Some extensions Real Options Analysis Studies and values this flexibility Real options are options where underlying value is a real asset not a financial asset as stock, bond, currency Flexibility in real investments means: changing cash flows along the way: profiting from opportunities, cutting off losses Discounted -
Master Thesis the Use of Interest Rate Derivatives and Firm Market Value an Empirical Study on European and Russian Non-Financial Firms
Master Thesis The use of Interest Rate Derivatives and Firm Market Value An empirical study on European and Russian non-financial firms Tilburg, October 5, 2014 Mark van Dijck, 937367 Tilburg University, Finance department Supervisor: Drs. J.H. Gieskens AC CCM QT Master Thesis The use of Interest Rate Derivatives and Firm Market Value An empirical study on European and Russian non-financial firms Tilburg, October 5, 2014 Mark van Dijck, 937367 Supervisor: Drs. J.H. Gieskens AC CCM QT 2 Preface In the winter of 2010 I found myself in the heart of a company where the credit crisis took place at that moment. During a treasury internship for Heijmans NV in Rosmalen, I experienced why it is sometimes unescapable to use interest rate derivatives. Due to difficult financial times, banks strengthen their requirements and the treasury department had to use different mechanism including derivatives to restructure their loans to the appropriate level. It was a fascinating time. One year later I wrote a bachelor thesis about risk management within energy trading for consultancy firm Tensor. Interested in treasury and risk management I have always wanted to finish my finance study period in this field. During the master thesis period I started to work as junior commodity trader at Kühne & Heitz. I want to thank Kühne & Heitz for the opportunity to work in the trading environment and to learn what the use of derivatives is all about. A word of gratitude to my supervisor Drs. J.H. Gieskens for his quick reply, well experienced feedback that kept me sharp to different levels of the subject, and his availability even in the late hours after I finished work. -
5. Caps, Floors, and Swaptions
Options on LIBOR based instruments Valuation of LIBOR options Local volatility models The SABR model Volatility cube Interest Rate and Credit Models 5. Caps, Floors, and Swaptions Andrew Lesniewski Baruch College New York Spring 2019 A. Lesniewski Interest Rate and Credit Models Options on LIBOR based instruments Valuation of LIBOR options Local volatility models The SABR model Volatility cube Outline 1 Options on LIBOR based instruments 2 Valuation of LIBOR options 3 Local volatility models 4 The SABR model 5 Volatility cube A. Lesniewski Interest Rate and Credit Models Options on LIBOR based instruments Valuation of LIBOR options Local volatility models The SABR model Volatility cube Options on LIBOR based instruments Interest rates fluctuate as a consequence of macroeconomic conditions, central bank actions, and supply and demand. The existence of the term structure of rates, i.e. the fact that the level of a rate depends on the maturity of the underlying loan, makes the dynamics of rates is highly complex. While a good analogy to the price dynamics of an equity is a particle moving in a medium exerting random shocks to it, a natural way of thinking about the evolution of rates is that of a string moving in a random environment where the shocks can hit any location along its length. A. Lesniewski Interest Rate and Credit Models Options on LIBOR based instruments Valuation of LIBOR options Local volatility models The SABR model Volatility cube Options on LIBOR based instruments Additional complications arise from the presence of various spreads between rates, as discussed in Lecture Notes #1, which reflect credit quality of the borrowing entity, liquidity of the instrument, or other market conditions. -
Interest Rate Modelling and Derivative Pricing
Interest Rate Modelling and Derivative Pricing Sebastian Schlenkrich HU Berlin, Department of Mathematics WS, 2019/20 Part III Vanilla Option Models p. 140 Outline Vanilla Interest Rate Options SABR Model for Vanilla Options Summary Swaption Pricing p. 141 Outline Vanilla Interest Rate Options SABR Model for Vanilla Options Summary Swaption Pricing p. 142 Outline Vanilla Interest Rate Options Call Rights, Options and Forward Starting Swaps European Swaptions Basic Swaption Pricing Models Implied Volatilities and Market Quotations p. 143 Now we have a first look at the cancellation option Interbank swap deal example Bank A may decide to early terminate deal in 10, 11, 12,.. years. p. 144 We represent cancellation as entering an opposite deal L1 Lm ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ T˜0 T˜k 1 T˜m − ✲ T0 TE Tl 1 Tn − ❄ ❄ ❄ ❄ ❄ ❄ K K [cancelled swap] = [full swap] + [opposite forward starting swap] K ✻ ✻ Tl 1 Tn − ✲ TE T˜k 1 T˜m − ❄ ❄ ❄ ❄ Lm p. 145 Option to cancel is equivalent to option to enter opposite forward starting swap K ✻ ✻ Tl 1 Tn − ✲ TE T˜k 1 T˜m − ❄ ❄ ❄ ❄ Lm ◮ At option exercise time TE present value of remaining (opposite) swap is n m Swap δ V (TE ) = K · τi · P(TE , Ti ) − L (TE , T˜j 1, T˜j 1 + δ) · τ˜j · P(TE , T˜j ) . − − i=l j=k X X future fixed leg future float leg | {z } | {z } ◮ Option to enter represents the right but not the obligation to enter swap. ◮ Rational market participant will exercise if swap present value is positive, i.e. Option Swap V (TE ) = max V (TE ), 0 . -
Seeking Income: Cash Flow Distribution Analysis of S&P 500
RESEARCH Income CONTRIBUTORS Berlinda Liu Seeking Income: Cash Flow Director Global Research & Design Distribution Analysis of S&P [email protected] ® Ryan Poirier, FRM 500 Buy-Write Strategies Senior Analyst Global Research & Design EXECUTIVE SUMMARY [email protected] In recent years, income-seeking market participants have shown increased interest in buy-write strategies that exchange upside potential for upfront option premium. Our empirical study investigated popular buy-write benchmarks, as well as other alternative strategies with varied strike selection, option maturity, and underlying equity instruments, and made the following observations in terms of distribution capabilities. Although the CBOE S&P 500 BuyWrite Index (BXM), the leading buy-write benchmark, writes at-the-money (ATM) monthly options, a market participant may be better off selling out-of-the-money (OTM) options and allowing the equity portfolio to grow. Equity growth serves as another source of distribution if the option premium does not meet the distribution target, and it prevents the equity portfolio from being liquidated too quickly due to cash settlement of the expiring options. Given a predetermined distribution goal, a market participant may consider an option based on its premium rather than its moneyness. This alternative approach tends to generate a more steady income stream, thus reducing trading cost. However, just as with the traditional approach that chooses options by moneyness, a high target premium may suffocate equity growth and result in either less income or quick equity depletion. Compared with monthly standard options, selling quarterly options may reduce the loss from the cash settlement of expiring calls, while selling weekly options could incur more loss. -
Implied Volatility Modeling
Implied Volatility Modeling Sarves Verma, Gunhan Mehmet Ertosun, Wei Wang, Benjamin Ambruster, Kay Giesecke I Introduction Although Black-Scholes formula is very popular among market practitioners, when applied to call and put options, it often reduces to a means of quoting options in terms of another parameter, the implied volatility. Further, the function σ BS TK ),(: ⎯⎯→ σ BS TK ),( t t ………………………………(1) is called the implied volatility surface. Two significant features of the surface is worth mentioning”: a) the non-flat profile of the surface which is often called the ‘smile’or the ‘skew’ suggests that the Black-Scholes formula is inefficient to price options b) the level of implied volatilities changes with time thus deforming it continuously. Since, the black- scholes model fails to model volatility, modeling implied volatility has become an active area of research. At present, volatility is modeled in primarily four different ways which are : a) The stochastic volatility model which assumes a stochastic nature of volatility [1]. The problem with this approach often lies in finding the market price of volatility risk which can’t be observed in the market. b) The deterministic volatility function (DVF) which assumes that volatility is a function of time alone and is completely deterministic [2,3]. This fails because as mentioned before the implied volatility surface changes with time continuously and is unpredictable at a given point of time. Ergo, the lattice model [2] & the Dupire approach [3] often fail[4] c) a factor based approach which assumes that implied volatility can be constructed by forming basis vectors. Further, one can use implied volatility as a mean reverting Ornstein-Ulhenbeck process for estimating implied volatility[5]. -
Forward Contracts and Futures a Forward Is an Agreement Between Two Parties to Buy Or Sell an Asset at a Pre-Determined Future Time for a Certain Price
Forward contracts and futures A forward is an agreement between two parties to buy or sell an asset at a pre-determined future time for a certain price. Goal To hedge against the price fluctuation of commodity. • Intension of purchase decided earlier, actual transaction done later. • The forward contract needs to specify the delivery price, amount, quality, delivery date, means of delivery, etc. Potential default of either party: writer or holder. Terminal payoff from forward contract payoff payoff K − ST ST − K K ST ST K long position short position K = delivery price, ST = asset price at maturity Zero-sum game between the writer (short position) and owner (long position). Since it costs nothing to enter into a forward contract, the terminal payoff is the investor’s total gain or loss from the contract. Forward price for a forward contract is defined as the delivery price which make the value of the contract at initiation be zero. Question Does it relate to the expected value of the commodity on the delivery date? Forward price = spot price + cost of fund + storage cost cost of carry Example • Spot price of one ton of wood is $10,000 • 6-month interest income from $10,000 is $400 • storage cost of one ton of wood is $300 6-month forward price of one ton of wood = $10,000 + 400 + $300 = $10,700. Explanation Suppose the forward price deviates too much from $10,700, the construction firm would prefer to buy the wood now and store that for 6 months (though the cost of storage may be higher). -
An Analysis of OTC Interest Rate Derivatives Transactions: Implications for Public Reporting
Federal Reserve Bank of New York Staff Reports An Analysis of OTC Interest Rate Derivatives Transactions: Implications for Public Reporting Michael Fleming John Jackson Ada Li Asani Sarkar Patricia Zobel Staff Report No. 557 March 2012 Revised October 2012 FRBNY Staff REPORTS This paper presents preliminary fi ndings and is being distributed to economists and other interested readers solely to stimulate discussion and elicit comments. The views expressed in this paper are those of the authors and are not necessarily refl ective of views at the Federal Reserve Bank of New York or the Federal Reserve System. Any errors or omissions are the responsibility of the authors. An Analysis of OTC Interest Rate Derivatives Transactions: Implications for Public Reporting Michael Fleming, John Jackson, Ada Li, Asani Sarkar, and Patricia Zobel Federal Reserve Bank of New York Staff Reports, no. 557 March 2012; revised October 2012 JEL classifi cation: G12, G13, G18 Abstract This paper examines the over-the-counter (OTC) interest rate derivatives (IRD) market in order to inform the design of post-trade price reporting. Our analysis uses a novel transaction-level data set to examine trading activity, the composition of market participants, levels of product standardization, and market-making behavior. We fi nd that trading activity in the IRD market is dispersed across a broad array of product types, currency denominations, and maturities, leading to more than 10,500 observed unique product combinations. While a select group of standard instruments trade with relative frequency and may provide timely and pertinent price information for market partici- pants, many other IRD instruments trade infrequently and with diverse contract terms, limiting the impact on price formation from the reporting of those transactions. -
Pricing of Index Options Using Black's Model
Global Journal of Management and Business Research Volume 12 Issue 3 Version 1.0 March 2012 Type: Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Inc. (USA) Online ISSN: 2249-4588 & Print ISSN: 0975-5853 Pricing of Index Options Using Black’s Model By Dr. S. K. Mitra Institute of Management Technology Nagpur Abstract - Stock index futures sometimes suffer from ‘a negative cost-of-carry’ bias, as future prices of stock index frequently trade less than their theoretical value that include carrying costs. Since commencement of Nifty future trading in India, Nifty future always traded below the theoretical prices. This distortion of future prices also spills over to option pricing and increase difference between actual price of Nifty options and the prices calculated using the famous Black-Scholes formula. Fisher Black tried to address the negative cost of carry effect by using forward prices in the option pricing model instead of spot prices. Black’s model is found useful for valuing options on physical commodities where discounted value of future price was found to be a better substitute of spot prices as an input to value options. In this study the theoretical prices of Nifty options using both Black Formula and Black-Scholes Formula were compared with actual prices in the market. It was observed that for valuing Nifty Options, Black Formula had given better result compared to Black-Scholes. Keywords : Options Pricing, Cost of carry, Black-Scholes model, Black’s model. GJMBR - B Classification : FOR Code:150507, 150504, JEL Code: G12 , G13, M31 PricingofIndexOptionsUsingBlacksModel Strictly as per the compliance and regulations of: © 2012.