Trading in energy futures and options plays a key role in hedging against fluctuations in the price of energy commodities, especially crude oil and natural gas. This long-awaited new edition highlights how exchange-traded futures and options markets work and how companies can successfully use the markets in their overall strategy to increase profitability. This wide-ranging new edition offers valuable insight for young professionals and students. Discussions on market efficiency, the role of commodities in Modern Portfolio Theory, and the NYMEX introduction of Clearport are all covered in this introduction to futures markets.
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Derivative securities and markets have experienced tremendous worldwide growth since 1970. But even so, they are not always well understood. To remedy this situation, the authors explain the link between options and futures and the underlying security or index from which they ultimately derive their value. Pricing and hedging relationships of futures contracts, option characteristics and strategies, and option pricing and hedging relationships are also addressed. To further assist the reader, the authors include exercises to reinforce the concepts as well as a glossary. The result is an updated look at options and futures that can benefit many of us.
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CONTENTS IN BRIEF List of Business Snapshots ........................................................................... xvPreface...................................................................................................... xvii1. Introduction..................................................................................................12. Mechanics of futures markets ....................................................................... 213. Hedging strategies using futures.................................................................... 454. Interest rates ............................................................................................... 735. Determination of forward and futures prices ................................................. 976. Interest rate futures.................................................................................... 1277. Swaps....................................................................................................... 1538. Mechanics of options markets .................................................................... 1859. Properties of stock options ......................................................................... 20910. Trading strategies involving options\hl} \hl 22911. Introduction to binomial trees .................................................................... 24712. Valuing stock options: The BlackScholes model ......................................... 26913. Options on stock indices and currencies ...................................................... 29514. Futures options ......................................................................................... 31115. The Greek letters....................................................................................... 32516. Binomial trees in practice ........................................................................... 35717. Volatility smiles ......................................................................................... 37918. Value at risk ............................................................................................. 39519. Interest rate options................................................................................... 42120. Exotic options and other nonstandard products........................................... 44321. Credit derivatives....................................................................................... 46122. Weather, energy, and insurance derivatives .................................................. 47723. Derivatives mishaps and what we can learn from them................................. 485Answers to Quiz Questions......................................................................... 497Glossary of terms ...................................................................................... 521DerivaGem software .................................................................................. 537Major exchanges trading futures and options............................................... 543Tables for Nx ......................................................................................... 545Index........................................................................................................ 547ContentsList of Business Snapshots .............................................................................................. xvPreface ....................................................................................................................... xviiChapter 1:Introduction .................................................................................................. 11.1 Futures Contracts ......................................................................................... 11.2 History of Futures Markets ........................................................................... 21.3 The Over-the-Counter Market........................................................................ 41.4 Forward Contracts ........................................................................................ 51.5 Options Contracts......................................................................................... 61.6 History of Options Markets........................................................................... 81.7 Types of Traders........................................................................................... 91.8 Hedgers ....................................................................................................... 91.9 Speculators................................................................................................. 131.10Arbitrageurs ............................................................................................... 151.11Dangers ..................................................................................................... 16Summary ................................................................................................... 17Further Reading ......................................................................................... 17Quiz .......................................................................................................... 18Questions and Problems .............................................................................. 18Assignment Questions ................................................................................. 19Chapter 2:Mechanics of Futures Markets...................................................................... 212.1 Opening and Closing Futures Positions ........................................................ 212.2 The Specication of a Futures Contract........................................................ 222.3 Convergence of Futures Price to Spot Price .................................................. 252.4 The Operation of Margins........................................................................... 262.5 Newspaper Quotes ...................................................................................... 302.6 Delivery ..................................................................................................... 332.7 Types of Traders and Types of Orders.......................................................... 342.8 Regulation.................................................................................................. 352.9 Accounting and Tax ................................................................................... 362.10Forward vs. Futures Contracts ..................................................................... 39Summary ................................................................................................... 41Further Reading ......................................................................................... 41Quiz .......................................................................................................... 42Questions and Problems .............................................................................. 42Assignment Questions ................................................................................. 43viiiContents Chapter 3:Hedging Strategies Using Futures .................................................................. 453.1Basic Principles........................................................................................... 453.2Arguments for and against Hedging ............................................................. 483.3Basis Risk .................................................................................................. 513.4Cross Hedging ............................................................................................ 563.5Stock Index Futures .................................................................................... 603.6Rolling the Hedge Forward.......................................................................... 65Summary.................................................................................................... 67Further Reading.......................................................................................... 68Quiz........................................................................................................... 69Questions and Problems............................................................................... 69Assignment Questions.................................................................................. 70Appendix: Proof of the Minimum Variance Hedge Ratio Formula................. 72Chapter 4:Interest Rates .............................................................................................. 734.1Types of Rates............................................................................................ 734.2Measuring Interest Rates ............................................................................. 754.3Zero Rates.................................................................................................. 774.4Bond Pricing .............................................................................................. 784.5Determining Treasury Zero Rates................................................................. 804.6Forward Rates ............................................................................................ 824.7Forward Rate Agreements ........................................................................... 844.8Theories of the Term Structure of Interest Rates ........................................... 87Summary.................................................................................................... 89Further Reading.......................................................................................... 90Quiz........................................................................................................... 90Questions and Problems............................................................................... 91Assignment Questions.................................................................................. 92Appendix: Exponential and Logarithm Functions ......................................... 94Chapter 5:Determination of Forward and Futures Prices ................................................. 975.1Investment Assets vs. Consumption Assets.................................................... 975.2Short Selling............................................................................................... 975.3Assumptions and Notation .......................................................................... 995.4Forward Price for an Investment Asset ......................................................... 995.5Known Income ......................................................................................... 1025.6Known Yield ............................................................................................ 1055.7Valuing Forward Contracts ........................................................................ 1055.8Are Forward Prices and Futures Prices Equal? ............................................ 1075.9Futures Prices of Stock Indices .................................................................. 1085.10Forward and Futures Contracts on Currencies............................................. 1105.11Futures on Commodities............................................................................ 1135.12The Cost of Carry..................................................................................... 1175.13Delivery Options ....................................................................................... 1175.14Futures Prices and Expected Spot Prices..................................................... 117Summary.................................................................................................. 119Further Reading........................................................................................ 121Quiz......................................................................................................... 121Questions and Problems............................................................................. 121ContentsixAssignment Questions ................................................................................123Appendix: Proof that Forward and Futures Prices Are Equal When InterestRates Are Constant ...................................................................125Chapter 6:Interest Rate Futures...................................................................................1276.1Day Count and Quotation Conventions.......................................................1276.2Treasury Bond Futures...............................................................................1306.3Eurodollar Futures.....................................................................................1356.4Duration ...................................................................................................1386.5Duration-Based Hedging Strategies Using Futures........................................142Summary ..................................................................................................147Further Reading ........................................................................................148Quiz .........................................................................................................148Questions and Problems .............................................................................148Assignment Questions ................................................................................150Chapter 7:Swaps .......................................................................................................1537.1Mechanics of Interest Rate Swaps ...............................................................1537.2Day Count Issues ......................................................................................1607.3Conrmations............................................................................................1607.4The Comparative-Advantage Argument .......................................................1617.5The Nature of Swap Rates .........................................................................1647.6Determining LIBOR/Swap Zero Rates ........................................................1657.7Valuation of Interest Rate Swaps ................................................................1667.8Currency Swaps .........................................................................................1707.9Valuation of Currency Swaps......................................................................1747.10Credit Risk ...............................................................................................1757.11Other Types of Swaps ................................................................................178Summary ..................................................................................................180Further Reading ........................................................................................181Quiz .........................................................................................................181Questions and Problems .............................................................................182Assignment Questions ................................................................................183Chapter 8:Mechanics of Options Markets ....................................................................1858.1Types of Options .......................................................................................1858.2Option Positions ........................................................................................1888.3Underlying Assets......................................................................................1908.4Specication of Stock Options ....................................................................1918.5Trading .....................................................................................................1958.6Commissions .............................................................................................1968.7Margins ....................................................................................................1978.8The Options Clearing Corporation ..............................................................1988.9Regulation.................................................................................................1998.10Taxation ...................................................................................................1998.11Warrants, Executive Stock Options, and Convertibles...................................2018.12Over-the-Counter Markets..........................................................................203Summary ..................................................................................................203Further Reading ........................................................................................204Contents Quiz......................................................................................................... 204Questions and Problems............................................................................. 205Assignment Questions................................................................................ 206Chapter 9:Properties of Stock Options........................................................................ 2099.1Factors Aecting Option Prices.................................................................. 2099.2Assumptions and Notation ........................................................................ 2139.3Upper and Lower Bounds for Option Prices ............................................... 2139.4PutCall Parity......................................................................................... 2179.5Early Exercise: Calls on a Non-Dividend-Paying Stock ................................ 2209.6Early Exercise: Puts on a Non-Dividend-Paying Stock ................................. 2229.7Eect of Dividends ................................................................................... 2239.8Summary.................................................................................................. 224Further Reading........................................................................................ 225Quiz......................................................................................................... 225Questions and Problems............................................................................. 226Assignment Questions................................................................................ 227Chapter 10:Trading Strategies Involving Options .......................................................... 22910.1Strategies Involving a Single Option and a Stock ....................................... 22910.2Spreads................................................................................................... 23110.3Combinations.......................................................................................... 24010.4Other Payos .......................................................................................... 24310.5Summary ................................................................................................ 243Further Reading...................................................................................... 244Quiz ....................................................................................................... 244Questions and Problems........................................................................... 244Assignment Questions .............................................................................. 245Chapter 11:Introduction to Binomial Trees .................................................................. 24711.1A One-Step Binomial Model .................................................................... 24711.2Risk-Neutral Valuation ............................................................................ 25011.3Two-Step Binomial Trees ......................................................................... 25211.4A Put Example ....................................................................................... 25511.5American Options ................................................................................... 25611.6Delta ...................................................................................................... 25711.7Determining u and d ............................................................................... 25811.8Increasing the Number of Time Steps ....................................................... 25911.9Options on Other Assets .......................................................................... 260Summary ................................................................................................ 265Further Reading...................................................................................... 265Quiz ....................................................................................................... 265Questions and Problems........................................................................... 266Assignment Questions .............................................................................. 267Chapter 12:Valuing Stock Options: The BlackScholes Model ...................................... 26912.1Assumptions about How Stock Prices Evolve ............................................ 26912.2Expected Return...................................................................................... 27212.3Volatility................................................................................................. 27412.4Estimating Volatility from Historical Data................................................. 274Contentsxi12.5Assumptions Underlying BlackScholes.....................................................27712.6The Key No-Arbitrage Argument..............................................................27812.7The BlackScholes Pricing Formulas.........................................................27912.8Risk-Neutral Valuation.............................................................................28112.9Implied Volatilities ...................................................................................28212.10Dividends ................................................................................................28312.11Valuing Executive Stock Options...............................................................285Summary.................................................................................................288Further Reading.......................................................................................289Quiz........................................................................................................290Questions and Problems............................................................................290Assignment Questions...............................................................................292Appendix: The Early Exercise of American Call Options onDividend-Paying Stocks ...........................................................293Chapter 13:Options on Stock Indices and Currencies.....................................................29513.1Options on Stock Indices..........................................................................29513.2Currency Options.....................................................................................29813.3Options on Stocks Paying Known Dividend Yields.....................................30013.4Valuation of Stock Index Options .............................................................30313.5Valuation of Currency Options .................................................................305Summary.................................................................................................307Further Reading.......................................................................................307Quiz........................................................................................................308Questions and Problems............................................................................308Assignment Questions...............................................................................309Chapter 14:Futures Options ........................................................................................31114.1Nature of Futures Options........................................................................31114.2Reasons for the Popularity of Futures Options...........................................31314.3European Spot and Futures Options..........................................................31414.4PutCall Parity........................................................................................31414.5Bounds for Futures Options......................................................................31614.6Valuation of Futures Options Using Binomial Trees ...................................31614.7A Futures Price as an Asset Providing a Yield ...........................................31814.8Black's Model for Valuing Futures Options ...............................................31914.9American Futures Options vs. American Spot Options ...............................320Summary.................................................................................................321Further Reading.......................................................................................321Quiz........................................................................................................322Questions and Problems............................................................................322Assignment Questions...............................................................................323Chapter 15:The Greek Letters ....................................................................................32515.1Illustration...............................................................................................32515.2Naked and Covered Positions....................................................................32615.3A Stop-Loss Strategy................................................................................32615.4Delta Hedging .........................................................................................32815.5Theta ......................................................................................................335xiiContents 15.6Gamma .................................................................................................. 33715.7Relationship between Delta, Theta, and Gamma........................................ 34015.8Vega....................................................................................................... 34115.9Rho........................................................................................................ 34315.10The Realities of Hedging.......................................................................... 34415.11Scenario Analysis .................................................................................... 34415.12Extension of Formulas............................................................................. 34615.13Creating Options Synthetically for Portfolio Insurance ............................... 34815.14Stock Market Volatility............................................................................ 350Summary ................................................................................................ 351Further Reading...................................................................................... 352Quiz ....................................................................................................... 352Questions and Problems........................................................................... 353Assignment Questions .............................................................................. 355Chapter 16:Binomial Trees in Practice ........................................................................ 35716.1The Binomial Model for a Non-Dividend-Paying Stock.............................. 35716.2Using the Binomial Tree for Options on Indices, Currencies, and FuturesContracts ................................................................................................ 36416.3The Binomial Model for a Dividend-Paying Stock ..................................... 36716.4Extensions of the Basic Tree Approach ..................................................... 36916.5Alternative Procedure for Constructing Trees ............................................. 37116.6Monte Carlo Simulation .......................................................................... 374Summary ................................................................................................ 375Further Reading...................................................................................... 376Quiz ....................................................................................................... 376Questions and Problems........................................................................... 376Assignment Questions .............................................................................. 377Chapter 17:Volatility Smiles ...................................................................................... 37917.1Foreign Currency Options........................................................................ 37917.2Equity Options........................................................................................ 38217.3The Volatility Term Structure and Volatility Surfaces ................................. 38417.4When a Single Large Jump Is Anticipated................................................. 386Summary ................................................................................................ 387Further Reading...................................................................................... 388Quiz ....................................................................................................... 389Questions and Problems........................................................................... 389Assignment Questions .............................................................................. 390Appendix: Why the Put Volatility Smile Is the Same Asthe Call Volatility Smile .......................................................... 392Chapter 18:Value at Risk .......................................................................................... 39518.1The VaR Measure ................................................................................... 39518.2Historical Simulation ............................................................................... 39818.3Model-Building Approach........................................................................ 39918.4Linear Model .......................................................................................... 40318.5Quadratic Model ..................................................................................... 40518.6Estimating Volatilities and Correlations ..................................................... 408Contentsxiii18.7Comparison of Approaches.......................................................................41218.8Stress Testing and Back Testing.................................................................413Summary.................................................................................................413Further Reading.......................................................................................414Quiz........................................................................................................415Questions and Problems............................................................................415Assignment Questions...............................................................................417Appendix: Cash-Flow Mapping ................................................................419Chapter 19:Interest Rate Options ................................................................................42119.1Exchange-Traded Interest Rate Options .....................................................42119.2Embedded Bond Options..........................................................................42319.3Black's Model..........................................................................................42319.4European Bond Options ...........................................................................42519.5Interest Rate Caps....................................................................................42719.6European Swap Options ...........................................................................43319.7Term Structure Models.............................................................................436Summary.................................................................................................437Further Reading.......................................................................................438Quiz........................................................................................................438Questions and Problems............................................................................439Assignment Questions...............................................................................440Chapter 20:Exotic Options and Other Nonstandard Products .........................................44320.1Exotic Options.........................................................................................44320.2Mortgage-Backed Securities ......................................................................44820.3Nonstandard Swaps..................................................................................450Summary.................................................................................................456Further Reading.......................................................................................457Quiz........................................................................................................458Questions and Problems............................................................................458Assignment Questions...............................................................................459Chapter 21:Credit Derivatives .....................................................................................46121.1Credit Default Swaps ...............................................................................46121.2Credit Indices ..........................................................................................46421.3Determining CDS Spreads ........................................................................46521.4Total Return Swaps..................................................................................47021.5CDS Forwards and Options......................................................................47121.6Collateralized Debt Obligations .................................................................471Summary.................................................................................................474Further Reading.......................................................................................474Quiz........................................................................................................475Questions and Problems............................................................................475Assignment Questions...............................................................................476Chapter 22:Weather, Energy, and Insurance Derivatives.................................................47722.1Weather Derivatives .................................................................................47722.2Energy Derivatives ...................................................................................47822.3Insurance Derivatives ...............................................................................481xivContents Summary ................................................................................................ 482Further Reading...................................................................................... 483Quiz ....................................................................................................... 483Questions and Problems........................................................................... 484Assignment Question ............................................................................... 484Chapter 23:Derivatives Mishaps and What We Can Learn from Them ........................... 48523.1Lessons for All Users of Derivatives ......................................................... 48523.2Lessons for Financial Institutions ............................................................. 48923.3Lessons for Nonnancial Corporations ..................................................... 493Summary ................................................................................................ 494Further Reading...................................................................................... 494Answers to Quiz Questions............................................................................................ 497Chapter 1 ............................................................................................... 497Chapter 2 ............................................................................................... 498Chapter 3 ............................................................................................... 498Chapter 4 ............................................................................................... 499Chapter 5 ............................................................................................... 501Chapter 6 ............................................................................................... 501Chapter 7 ............................................................................................... 502Chapter 8 ............................................................................................... 504Chapter 9 ............................................................................................... 506Chapter 10.............................................................................................. 506Chapter 11.............................................................................................. 507Chapter 12.............................................................................................. 509Chapter 13.............................................................................................. 510Chapter 14.............................................................................................. 512Chapter 15.............................................................................................. 512Chapter 16.............................................................................................. 513Chapter 17.............................................................................................. 515Chapter 18.............................................................................................. 515Chapter 19.............................................................................................. 517Chapter 20.............................................................................................. 517Chapter 21.............................................................................................. 518Chapter 22.............................................................................................. 519Glossary of Terms........................................................................................................ 521DerivaGem Software .................................................................................................... 537The Options Calculator............................................................................ 537The Applications Builder ......................................................................... 540Major Exchanges Trading Futures and Options ............................................................... 543Table for Nx When x 6 0........................................................................................... 544Table for Nx When x > 0........................................................................................... 545Index .......................................................................................................................... 547BUSINESS SNAPSHOTS Hedge Funds .................................................................................................... 10The Barings Bank Disaster ................................................................................ 17The Unanticipated Delivery of a Futures Contract............................................... 23Long-Term Capital Management's Big Loss........................................................ 30Hedging by Gold Mining Companies ................................................................. 51Metallgesellschaft: Hedging Gone Awry.............................................................. 67What is the Risk-Free Rate? .............................................................................. 75Orange County's Yield Curve Plays .................................................................... 84Expensive Failures of Financial Institutions in the U.S. ....................................... 89Kidder Peabody's Embarrassing Mistake ...........................................................102A Systems Error? .............................................................................................107The CME Nikkei 225 Futures Contract .............................................................109Index Arbitrage in October 1987 .......................................................................110Day Counts Can Be Deceptive ..........................................................................128The Wild Card Play .........................................................................................133AssetLiability Management by Banks..............................................................143Extract from Hypothetical Swap Conrmation ...................................................161The Hammersmith and Fulham Story ...............................................................178Gucci Group's Large Dividend .........................................................................194Tax Planning with Options ...............................................................................201Executive Stock Options ...................................................................................202PutCall Parity and Capital Structure ...............................................................219Losing Money with Box Spreads .......................................................................236How to Make Money from Trading Straddles ....................................................241Mutual Fund Returns Can Be Misleading..........................................................273What Causes Volatility?....................................................................................277Executive Stock Options and Dilution ...............................................................287Can We Guarantee that Stocks Will Beat Bonds in the Long Run? .....................305Dynamic Hedging in Practice............................................................................345Was Portfolio Insurance to Blame for the Crash of 1987? ...................................351Making Money from Foreign Currency Options .................................................382Crashophobia ..................................................................................................384How Bank Regulators Use VaR........................................................................396PutCall Parity for Caps and Floors.................................................................430Swaptions and Bond Options............................................................................433Hypothetical Conrmation for Nonstandard Swap .............................................451Hypothetical Conrmation for Compounding Swap............................................452Hypothetical Conrmation for Equity Swap.......................................................454Procter & Gamble's Bizarre Deal ......................................................................456Who Bears the Credit Risk?..............................................................................462Is the CDS Market a Fair Game? .....................................................................469Big Losses by Financial Institutions...................................................................486Big Losses by Nonnancial Organizations..........................................................487