Options, futures, and other derivatives

929 Pages·2016·10.168 MB·English

by  Basu, Sankarshan, Hull, John

N I N T H E D I T I O N
OPTIONS, FUTURES,
AND OTHER DERIVATIVES
John C. Hull
Maple Financial Group Professor of Derivatives and Risk Management
Joseph L. Rotman School of Management
University of Toronto
Sankarshan Basu
Professor, Finance and Control
Indian Institute of Management Bangalore
Chennai(cid:2)Delhi
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CONTENTS IN BRIEF
List of Business Snapshots............................................................................xvi
List of Technical Notes................................................................................xviii
Preface.......................................................................................................xix
1. Introduction...................................................................................................1
2. Mechanics of futures markets.........................................................................31
3. Hedging strategies using futures......................................................................63
4. Interest rates................................................................................................92
5. Determination of forward and futures prices................................................... 123
6. Interest rate futures..................................................................................... 153
7. Swaps....................................................................................................... 175
8. Securitization and the credit crisis of 2007...................................................... 210
9. OIS discounting, credit issues, and funding costs............................................. 225
10. Mechanics of options markets...................................................................... 239
11. Properties of stock options........................................................................... 262
12. Trading strategies involving options............................................................... 282
13. Binomial trees............................................................................................ 302
14. Wiener processes and Itoˆ’s lemma................................................................. 330
15. The Black–Scholes–Merton model................................................................ 349
16. Employee stock options............................................................................... 382
17. Options on stock indices and currencies......................................................... 395
18. Futures options.......................................................................................... 411
19. The Greek letters........................................................................................ 427
20. Volatility smiles.......................................................................................... 459
21. Basic numerical procedures.......................................................................... 478
22. Value at risk.............................................................................................. 522
23. Estimating volatilities and correlations........................................................... 550
24. Credit risk................................................................................................. 573
25. Credit derivatives........................................................................................ 601
26. Exotic options............................................................................................ 629
27. More on models and numerical procedures..................................................... 656
28. Martingales and measures............................................................................ 687
29. Interest rate derivatives: The standard market models....................................... 705
30. Convexity, timing, and quanto adjustments..................................................... 726
31. Interest rate derivatives: Models of the short rate............................................. 739
32. HJM, LMM, and multiple zero curves........................................................... 773
33. Swaps Revisited.......................................................................................... 793
34. Energy and commodity derivatives................................................................ 808
35. Real options.............................................................................................. 826
36. Derivatives mishaps and what we can learn from them..................................... 840
Glossary of terms....................................................................................... 854
DerivaGem software.................................................................................... 876
Majorexchanges trading futures and options.................................................. 881
Tables for NðxÞ........................................................................................... 882
Author index.............................................................................................. 884
Subject index.............................................................................................. 888
iv
Contents
List of Business Snapshots...............................................................................xvi
List of Technical Notes.................................................................................xviii
Preface.......................................................................................................xix
Chapter 1. Introduction....................................................................................................1
1.1 Exchange-traded markets........................................................................2
1.2 Over-the-counter markets........................................................................3
1.3 Forward contracts..................................................................................6
1.4 Futures contracts...................................................................................8
1.5 Options................................................................................................8
1.6 Types of traders................................................................................... 11
1.7 Hedgers.............................................................................................. 12
1.8 Speculators......................................................................................... 14
1.9 Arbitrageurs........................................................................................ 17
1.10 Overview of the Indian derivatives market............................................... 17
1.11 Dangers............................................................................................. 25
Summary............................................................................................ 26
Further reading................................................................................... 27
Practice questions................................................................................. 27
Further questions................................................................................. 29
Chapter 2. Mechanics of futures markets........................................................................... 31
2.1 Background........................................................................................ 31
2.2 Specification of afutures contract........................................................... 36
2.3 Convergence of futures price to spot price............................................... 41
2.4 The operation of margin accounts.......................................................... 41
2.5 OTC markets...................................................................................... 45
2.6 Newspaper quotes................................................................................ 48
2.7 Delivery............................................................................................. 51
2.8 Types of traders and types of orders....................................................... 52
2.9 Regulation.......................................................................................... 53
2.10 Accounting and tax.............................................................................. 54
2.11 Forward vs. futures contracts................................................................. 56
2.12 Issue of credit risk and OTC markets in India-differences with
international markets............................................................................ 57
Summary............................................................................................ 58
Further reading................................................................................... 59
Practice questions................................................................................. 59
Further questions................................................................................. 61
v
vi Contents
Chapter 3. Hedging strategies using futures........................................................................63
3.1 Basic principles....................................................................................63
3.2 Arguments for and against hedging.........................................................65
3.3 Basis risk............................................................................................69
3.4 Cross hedging......................................................................................72
3.5 Stock index futures...............................................................................76
3.6 Stack and roll......................................................................................82
Summary............................................................................................84
Further reading....................................................................................85
Practice questions.................................................................................86
Further questions.................................................................................88
Appendix: Capital asset pricing model....................................................90
Chapter 4. Interest rates.................................................................................................92
4.1 Types of rates......................................................................................92
4.2 Measuring interest rates........................................................................97
4.3 Zero rates......................................................................................... 100
4.4 Bond pricing..................................................................................... 100
4.5 Determining Treasury zero rates........................................................... 102
4.6 Forward rates.................................................................................... 104
4.7 Forward rate agreements..................................................................... 106
4.8 Duration........................................................................................... 110
4.9 Convexity.......................................................................................... 114
4.10 Theories of the term structure of interest rates........................................ 115
Summary.......................................................................................... 118
Further reading.................................................................................. 118
Practice questions............................................................................... 119
Further questions............................................................................... 121
Chapter 5. Determination of forward and futures prices...................................................... 123
5.1 Investment assets vs. consumption assets............................................... 123
5.2 Short selling...................................................................................... 124
5.3 Assumptions and notation................................................................... 125
5.4 Forward price for an investment asset................................................... 126
5.5 Known income.................................................................................. 130
5.6 Known yield...................................................................................... 132
5.7 Valuing forward contracts................................................................... 133
5.8 Are forward prices and futures prices equal?.......................................... 134
5.9 Futures prices of stock indices.............................................................. 135
5.10 Forward and futures contracts on currencies.......................................... 138
5.11 Futures on commodities...................................................................... 141
5.12 The cost of carry................................................................................ 144
5.13 Delivery options................................................................................. 145
5.14 Futures prices and expected future spot prices........................................ 145
Summary.......................................................................................... 147
Further reading.................................................................................. 149
Practice questions............................................................................... 149
Further questions............................................................................... 151
Chapter 6. Interest rate futures...................................................................................... 153
6.1 Day count and quotation conventions................................................... 153
6.2 Treasury bond futures......................................................................... 156
6.3 Eurodollar futures.............................................................................. 162
6.4 Duration-based hedging strategies using futures...................................... 168
Contents vii
6.5 Hedging portfolios of assets and liabilities..............................................169
Summary...........................................................................................170
Further reading..................................................................................171
Practice questions................................................................................171
Further questions................................................................................173
Chapter 7. Swaps.........................................................................................................175
7.1 Mechanics of interest rate swaps...........................................................178
7.2 Day count issues.................................................................................183
7.3 Confirmations....................................................................................184
7.4 The comparative-advantage argument....................................................185
7.5 The nature of swap rates......................................................................188
7.6 Determining the LIBOR/swap zero rates................................................189
7.7 Valuation of interest rate swaps.............................................................189
7.8 Term structure effects..........................................................................193
7.9 Fixed-for-fixed currency swaps..............................................................193
7.10 Valuation of fixed-for-fixed currency swaps.............................................197
7.11 Other currencyswaps..........................................................................200
7.12 Credit risk.........................................................................................201
7.13 Other types of swaps...........................................................................203
Summary...........................................................................................205
Further reading..................................................................................206
Practice questions................................................................................206
Further questions................................................................................208
Chapter 8. Securitization and the credit crisis of 2007........................................................210
8.1 Securitization.....................................................................................210
8.2 The US housing market.......................................................................214
8.3 What went wrong?..............................................................................218
8.4 The aftermath....................................................................................220
8.5 Impact of the crisis in India.................................................................221
Summary...........................................................................................222
Further reading..................................................................................223
Practice questions................................................................................223
Further questions................................................................................224
Chapter 9. OIS discounting, credit issues, and funding costs................................................225
9.1 The risk-free rate................................................................................225
9.2 The OIS rate......................................................................................227
9.3 Valuing swaps and FRAs with OIS discounting......................................230
9.4 OIS vs. LIBOR: Which is correct?.........................................................231
9.5 Credit risk: CVA and DVA..................................................................232
9.6 Funding costs.....................................................................................234
Summary...........................................................................................236
Further reading..................................................................................236
Practice questions................................................................................237
Further questions................................................................................237
Chapter 10. Mechanics of options markets.........................................................................239
10.1 Types of options.................................................................................239
10.2 Option positions.................................................................................242
10.3 Underlying assets................................................................................244
10.4 Specification of stock options...............................................................245
10.5 Trading.............................................................................................249
10.6 Commissions......................................................................................251
viii Contents
10.7 Margin requirements........................................................................... 252
10.8 The options clearing corporation.......................................................... 253
10.9 Regulation........................................................................................ 254
10.10 Taxation........................................................................................... 254
10.11 Warrants, employee stock options, and convertibles................................. 256
10.12 Over-the-counter options markets......................................................... 257
Summary.......................................................................................... 258
Further reading.................................................................................. 258
Practice questions............................................................................... 259
Further questions............................................................................... 260
Chapter 11. Properties of stockoptions............................................................................. 262
11.1 Factors affecting option prices.............................................................. 262
11.2 Assumptions and notation................................................................... 266
11.3 Upper and lower bounds for option prices............................................. 266
11.4 Put–call parity................................................................................... 269
11.5 Calls on a non-dividend-paying stock.................................................... 273
11.6 Puts on a non-dividend-paying stock..................................................... 274
11.7 Effect of dividends............................................................................. 277
Summary.......................................................................................... 278
Further reading.................................................................................. 279
Practice questions............................................................................... 279
Further questions............................................................................... 281
Chapter 12. Trading strategies involving options.................................................................. 282
12.1 Principal-protected notes..................................................................... 282
12.2 Trading an option and the underlying asset........................................... 284
12.3 Spreads............................................................................................. 286
12.4 Combinations.................................................................................... 294
12.5 Other payoffs..................................................................................... 297
Summary.......................................................................................... 298
Further reading.................................................................................. 299
Practice questions............................................................................... 299
Further questions............................................................................... 300
Chapter 13. Binomial trees............................................................................................. 302
13.1 A one-step binomial model and a no-arbitrage argument......................... 302
13.2 Risk-neutral valuation......................................................................... 306
13.3 Two-step binomial trees...................................................................... 308
13.4 A put example................................................................................... 311
13.5 American options............................................................................... 312
13.6 Delta................................................................................................ 313
13.7 Matching volatility with u and d........................................................... 314
13.8 The binomial tree formulas.................................................................. 316
13.9 Increasing the number of steps............................................................. 316
13.10 Using DerivaGem.............................................................................. 317
13.11 Options on other assets....................................................................... 318
Summary.......................................................................................... 321
Further reading.................................................................................. 322
Practice questions............................................................................... 323
Further questions............................................................................... 324
Appendix: Derivation of the Black–Scholes–Merton option-pricing
formula from a binomial tree................................................ 326
Contents ix
Chapter 14. Wiener processes and Itoˆ’s lemma....................................................................330
14.1 The Markov property..........................................................................330
14.2 Continuous-time stochastic processes.....................................................331
14.3 The process for a stock price................................................................336
14.4 The parameters...................................................................................339
14.5 Correlated processes............................................................................340
14.6 Itoˆ’s lemma........................................................................................341
14.7 The lognormal property.......................................................................342
Summary...........................................................................................343
Further reading..................................................................................344
Practice questions................................................................................344
Further questions................................................................................345
Appendix: Derivation of Itoˆ’s lemma.....................................................347
Chapter 15. The Black–Scholes–Merton model..................................................................349
15.1 Lognormal property of stock prices.......................................................350
15.2 The distribution of the rate of return.....................................................351
15.3 The expected return.............................................................................352
15.4 Volatility...........................................................................................353
15.5 The idea underlying the Black–Scholes–Merton differential equation.........357
15.6 Derivation of the Black–Scholes–Merton differential equation..................359
15.7 Risk-neutral valuation.........................................................................362
15.8 Black–Scholes–Merton pricing formulas................................................363
15.9 Cumulative normal distribution function................................................366
15.10 Warrants and employee stock options....................................................367
15.11 Implied volatilities...............................................................................369
15.12 Dividends..........................................................................................371
Summary...........................................................................................374
Further reading..................................................................................375
Practice questions................................................................................376
Further questions................................................................................378
Appendix: Proof of the Black–Scholes–Merton formula using
risk-neutral valuation...........................................................380
Chapter 16. Employee stockoptions..................................................................................382
16.1 Contractual arrangements.....................................................................382
16.2 Do options align the interests of shareholders and managers?....................384
16.3 Accounting issues...............................................................................385
16.4 Valuation...........................................................................................386
16.5 Backdating scandals............................................................................391
Summary...........................................................................................392
Further reading..................................................................................393
Practice questions................................................................................393
Further questions................................................................................394
Chapter 17. Options on stock indices and currencies............................................................395
17.1 Options on stock indices......................................................................395
17.2 Currencyoptions................................................................................397
17.3 Options on stocks paying known dividend yields.....................................400
17.4 Valuation of European stock index options.............................................402
17.5 Valuation of European currencyoptions.................................................405
17.6 American options...............................................................................406
Summary...........................................................................................407
Further reading..................................................................................407