Derivatives

KEITH CUTHBERTSON is professor of Finance at CASS Business School, City, University of London. He has worked at H.M.Treasury, Bank of England, National Institute of Economic and Social Research NIESR and at business schools at Imperial College London and the University of Newcastle. DIRK NITZSCHE is Senior Lecturer in Finance, Course Director for the Quants Masters Programmes, and Associate Dean for International Relations at CASS Business School, City, University of London. NIALL O' SULLIVAN is professor of economics at Cork University Business School, University College Cork and former adjunct lecturer at Dublin City University Business School.

• About the Authors xxviiAbout the Companion Site xxixPreface xxxiChapter 1 Derivative Securities 11.1 Forwards and Futures 21.2 Options 71.3 Swaps 141.4 Hedging, Speculation, and Arbitrage 161.5 Short-Selling 181.6 Summary 20Exercises 21Part I Forwards and Futures 23Chapter 2 Futures Markets 252.1 Trading on Futures Markets 252.2 Futures Exchanges and Traders 292.3 Margins and Marking-to-Market 302.4 Summary 36Exercises 36Chapter 3 Forward and Futures Prices 393.1 Pricing Forward Contracts 393.2 Dividends, Storage Costs, and Convenience Yield 463.3 Commodity Futures 493.4 Value of a Forward Contract 533.5 Summary 57Exercises 57Chapter 4 Futures: Hedging and Speculation 594.1 Hedging Using Futures 594.2 Novel Futures Contracts 674.3 Speculation 704.4 Summary 72Exercises 73Chapter 5 Index Futures 755.1 Stock Index Futures (SIF) 765.2 Index Arbitrage 785.3 Hedging 815.4 Tailing the Hedge 885.5 Summary 89Appendix 5: Hedge Ratios 89Exercises 93Chapter 6 Strategies: Stock Index Futures 956.1 Underpriced Stocks: Hedging Market Risk 956.2 Overpriced Stocks: Hedging Market Risk 986.3 Market-neutral Hedge Fund 1006.4 Long-Short Hedge Fund 1016.5 Changing Stock Market Exposure 1046.6 Merger Arbitrage 1066.7 Summary 109Appendix 6.A: Stock Picking and Market Risk 110Appendix 6.B: Market Timing 112Appendix 6.C: Hedging: Long-Short Portfolio 114Appendix 6.D: Merger Arbitrage and Hedging 116Exercises 117Chapter 7 Currency Forwards and Futures 1197.1 FX-Futures Contracts 1207.2 Pricing FX-Forward Contracts 1237.3 Pricing FX-Futures Contracts 1267.4 Hedging and Speculation: Forwards 1277.5 Hedging and Speculation: Futures 1297.6 Summary 132Appendix 7: Hedging Using FX-Futures 133Exercises 135Part II Fixed Income: Cash Markets 137Chapter 8 Interest Rates 1398.1 LIBOR, Repos, Fed Funds, and OIS Rates 1398.2 Day-Count Conventions 1418.3 Forward Rates 1468.4 Forward Rate Agreements (FRAs) 1508.5 Summary 154Exercises 154Chapter 9 Bond Markets 1579.1 Prices, Yields, and Return 1589.2 Pricing Coupon Bonds 1659.3 Summary 168Exercises 169Chapter 10 Bonds: Duration and Convexity 17110.1 Yield Curve 17110.2 Duration and Convexity 17310.3 Summary 178Appendix 10: Duration and Convexity 179Exercises 181Part III Fixed Income Futures Contracts 183Chapter 11 Interest Rate Futures 18511.1 Three-month Eurodollar Futures Contract 18611.2 Sterling 3-month Futures Contract 18811.3 T-bill Futures 18811.4 Futures Price and Forward Rates 18911.5 Pricing Interest Rate Futures 19011.6 Arbitrage: Implied Repo Rate 19311.7 Speculation 19511.8 Spread Trades 19611.9 Summary 199Appendix 11.A: Futures Prices and Interest Rates 200Exercises 203Chapter 12 Hedging with Interest Rate Futures 20512.1 Number of Futures Contracts 20612.2 Different Types of Hedge 21012.3 Hedging: T-bill and Eurodollar Futures 21412.4 Eurodollar Stack Hedge 21712.5 Summary 221Appendix 12: Hedge Ratios 222Exercises 224Chapter 13 T-bond Futures 22713.1 Contract Specifications 22813.2 Conversion Factor and Cheapest-to-Deliver 23013.3 Hedging Using T-Bonds 23413.4 Hedging: Further Issues 23513.5 Market Timing 23813.6 Wild Card Play 23913.7 Pricing T-bond Futures 24013.8 T-bond Futures Spreads 24413.9 Summary 247Appendix 13.A: Hedging: Duration and Market Timing 248Appendix 13.B: Implied Repo Rate and Arbitrage 250Exercises 251Part IV Options 253Chapter 14 Options Markets 25514.1 Market Organisation 25514.2 Call Options 26114.3 Put Options 26814.4 Intrinsic Value and Time Value 27314.5 Summary 276Exercises 277Chapter 15 Uses of Options 27915.1 Protective Put 27915.2 Put–Call Parity: European Options 28215.3 Guaranteed Bond 28315.4 Other Options 28615.5 Summary 288Exercises 289Chapter 16 Black–Scholes Model 29116.1 Determinants of Option Prices 29116.2 Black–Scholes 29616.3 Are Stocks Less Risky in the Long Run? 30316.4 Delta Hedging 30616.5 Implied Volatility 30816.6 Summary 311Appendix 16: Price Bounds on European Options 312Exercises 313Chapter 17 Option Strategies 31517.1 Synthetic Securities 31617.2 Bull and Bear Spreads 32017.3 Straddle, Strangle, Butterfly, and Condor 32417.4 Horizontal (Time, Calendar) Spreads 33317.5 Summary 335Exercises 335Chapter 18 Stock Options and Stock Index Options 33718.1 Options on Stocks 33718.2 Stock Index Options (SIO) 34218.3 Summary 345Appendix 18.A: Static Hedge: Index Puts 345Appendix 18.B: Dynamic Delta Hedge 346Exercises 346Chapter 19 Foreign Currency Options 34919.1 Contract Specifications 34919.2 Speculation 35019.3 Hedging Foreign Currency Exposure 35319.4 Other Currency Options 35819.5 Summary 358Exercises 359Chapter 20 Options on Futures 36320.1 Market Conventions 36320.2 Price Bounds on European Futures Options 36620.3 Trading Strategies 36720.4 Summary 370Exercises 371Part V Options Pricing 373Chapter 21 BOPM: Introduction 37521.1 One-Period BOPM 37521.2 Risk-neutral Valuation 37921.3 Determinants of Call Premium 38221.4 Pricing a European Put Option 38321.5 Summary 384Appendix 21: No-arbitrage Conditions 385Exercises 386Chapter 22 BOPM: Implementation 38922.1 Generalising the BOPM 39022.2 Replication Portfolio 39322.3 BOPM to Black–Scholes 39622.4 Summary 398Appendix 22: Delta Hedging and Arbitrage 399Exercises 402Chapter 23 BOPM: Extensions 40523.1 American Options 40523.2 Options on Other Underlying Assets 40723.3 Options on Futures Contracts 40923.4 Options on Dividend-paying Stocks 41223.5 Summary 414Appendix 23: BOPM and Risk-neutral Valuation 415Exercises 419Chapter 24 Analysis of Black–Scholes 42124.1 Volatility 42124.2 Testing Black–Scholes 42524.3 Limitations of Black–Scholes 42824.4 Summary 431Exercises 432Chapter 25 Pricing European Options 43525.1 What do N(d1) and N(d2) Represent? 43525.2 European Options: Dividend Paying Stocks 43625.3 Foreign Currency and Futures Options 43725.4 Put–Call Parity 44025.5 Summary 443Exercises 444Chapter 26 Pricing Options: Monte Carlo Simulation 44726.1 Brownian Motion: Parallel Universe 44726.2 Pricing a European Call 44926.3 Variance Reduction Methods 45426.4 The Greeks 45526.5 Multiple Stochastic Factors 45626.6 Path-dependent Options 45926.7 Summary 460Appendix 26: MCS, Several Stochastic Variables 461Exercises 464Part VI The Greeks 467Chapter 27 Delta Hedging 46927.1 Delta 46927.2 Dynamic Delta Hedging 47327.3 Summary 481Exercises 481Chapter 28 The Greeks 48328.1 Different Greeks 48328.2 Hedging with the Greeks 49128.3 Greeks and the BOPM 49628.4 Summary 498Appendix 28: Black–Scholes and the Greeks 499Exercises 502Chapter 29 Portfolio Insurance 50329.1 Static Hedge 50429.2 Dynamic Portfolio Insurance 50729.3 Summary 513Exercises 514Part VII Advanced Options 517Chapter 30 Other Options 51930.1 Corporate Equity and Debt 51930.2 Warrants 52230.3 Equity Collar 52430.4 Summary 526Exercises 527Chapter 31 Exotic Options 52931.1 Three-period BOPM 53031.2 Asian Options 53131.3 Other Exotics: Lookbacks, Barrier, Compound, and Chooser 53531.4 Summary 542Exercises 543Chapter 32 Energy and Weather Derivatives 54532.1 Energy Contracts 54632.2 Hedging with Energy Futures 54932.3 Energy Swaps 55232.4 Weather Derivatives 55732.5 Reinsurance and CAT Bonds 56232.6 Summary 562Exercises 563Part VIII Swaps 567Chapter 33 Interest Rate Swaps 56933.1 Using Interest Rate Swaps 57133.2 Cash Flows in a Swap 57333.3 Settlement and Price Quotes 57533.4 Terminating a Swap 57733.5 Comparative Advantage 57733.6 Summary 581Appendix 33: Comparative Advantage with Swap Dealer 581Exercises 583Chapter 34 Pricing Interest Rate Swaps 58534.1 Cash Flows in a Swap 58634.2 Floating Rate Note (FRN) 58734.3 Pricing a Swap: Short Method 58934.4 Pricing a Swap: Forward Rate Method 59134.5 Market Value of a Swap 59334.6 Swap Delta and PVBP 59634.7 Summary 597Appendix 34: Value of an FRN Using Arbitrage 597Exercises 598Chapter 35 Other Interest Rate Swaps 60135.1 Swap Deals 60135.2 Pricing Non-standard Swaps 60335.3 Hedging Interest Rate Swaps 60835.4 Credit Risk 61435.5 Summary 615Exercises 616Chapter 36 Currency Swaps 61736.1 Uses 61736.2 Pricing a Fixed-Fixed Currency Swap 62036.3 Valuing a Fixed-Fixed Currency Swap 62236.4 Summary 625Appendix 36.A: Pricing a Currency Swap 626Appendix 36.B: Valuation of a Currency Swap 628Exercises 629Chapter 37 Equity Swaps 63137.1 Equity-for-LIBOR: Fixed Notional Principal 63237.2 Unhedged Cross-currency Equity Swap 63437.3 Hedged Cross-currency Equity Swap 63537.4 Pricing Equity Swaps 63637.5 Summary 643Appendix 37: Valuation of Equity-for-LIBOR Swap 643Exercises 644Part IX Fixed Income Derivatives 647Chapter 38 T-Bond Option, Caps, Floors and Collar 64938.1 Options on T-Bonds and Eurodollars 64938.2 Caplets and Floorlets 65038.3 Interest Rate Cap 65538.4 Interest Rate Floor 65738.5 Interest Rate Collar 65838.6 Summary 661Exercises 662Chapter 39 Swaptions, Forward Swaps, and MBS 66539.1 Swaptions 66539.2 Forward Swaps 66839.3 Mortgage-backed Securities (MBS) 67039.4 Hedging Fixed Income Derivatives 67539.5 Summary 677Exercises 678Chapter 40 Pricing Fixed Income Options: Black’s Model and MCS 68140.1 Black’s Model: European Options 68240.2 Pricing a Caplet Using MCS 68440.3 European Swaption: Black’s Model 68540.4 Summary 688Exercises 688Chapter 41 Pricing Fixed Income Derivatives: BOPM 69141.1 No-arbitrage Approach: BOPM 69241.2 Pricing a Coupon Bond 69741.3 Pricing Options 69741.4 Pricing a Callable Bond 70041.5 Pricing Caps 70141.6 Pricing FRAs 70241.7 Pricing a Swaption 70441.8 Pricing FRNs with Embedded Options 70541.9 More Lattices 70841.10 Summary 709Exercises 710Part X Credit Derivatives 713Chapter 42 Credit Default Swaps (CDS) 71542.1 Credit Risk and CDS 71642.2 Speculation with CDS 71742.3 Contract Details 71942.4 Pricing and Valuation 72042.5 Bond Yields and the CDS Spread 72542.6 Credit Indices and other CDS Contracts 72742.7 Derivatives on the CDS Spread 72742.8 Summary 729Exercises 730Chapter 43 Securitisation, ABSs and CDOs 73143.1 ABSs and ABS-CDOs 73143.2 Credit Enhancement 73643.3 Losses on ABSs and ABS-CDOs 73843.4 Sub-prime Crisis 2007–8 74043.5 Synthetic CDOs 74343.6 Single Tranche Trading 74443.7 Total Return Swap 74643.8 Summary 747Exercises 748Part XI Market Risk 749Chapter 44 Value at Risk 75144.1 Introduction 75144.2 Value at Risk (VaR) 75244.3 Forecasting Volatility 76144.4 Backtesting 76344.5 Capital Adequacy 76644.6 Summary 767Exercises 768Chapter 45 VaR: Other Portfolios 76945.1 Single Index Model 76945.2 VaR for Coupon Bonds 77345.3 VaR: Options 77745.4 Summary 779Appendix 45.A: VaR for Foreign Assets 779Appendix 45.B: Single Index Model (SIM) 780Appendix 45.C: Cash Flow Mapping 782Exercises 784Chapter 46 VaR: Alternative Measures 78746.1 Historical Simulation 78746.2 Bootstrapping 79246.3 Monte Carlo Simulation 79546.4 Alternative Methods 79946.5 Summary 803Exercises 804Part XII Price Dynamics 807Chapter 47 Asset Price Dynamics 80947.1 Stochastic Processes 81047.2 Geometric Brownian Motion (GBM) and Ito’s Lemma 81247.3 Distribution of Log Stock Price and Stock Price 81447.4 Summary 817Appendix 47: Ito’s Lemma 817Exercises 818Chapter 48 Black–Scholes PDE 82148.1 Risk-Neutral Valuation and Black–Scholes PDE 82148.2 Finite Difference Methods 82648.3 Summary 830Appendix 48: Derivation of Black–Scholes PDE 830Exercises 833Chapter 49 Equilibrium Models: Term Structure 83549.1 Risk-neutral Valuation 83649.2 Models of the Short-Rate 83749.3 Pricing Using Continuous Time Models 83949.4 Bond Prices and Derivative Prices 84149.5 Summary 843Exercises 844Glossary 845Bibliography 867Author Index 871Subject Index 873