Options, Futures, and Other Derivatives

Cover......Page 1
About Pearson......Page 2
Title Page ......Page 4
Copyright Page......Page 5
Detication Page ......Page 6
CONTENTS IN BRIEF......Page 7
Contents......Page 8
BUSINESS SNAPSHOTS......Page 19
TECHNICAL NOTES......Page 20
 What’s New in the Tenth Edition?......Page 21
 Instructor Resources......Page 22
 Acknowledgments......Page 23
About the Author......Page 24
About the Adapter......Page 25
Chapter 1 - Introduction......Page 26
 1.1 EXCHANGE-TRADED MARKETS......Page 27
 1.2 OVER-THE-COUNTER MARKETS......Page 28
 1.3 FORWARD CONTRACTS......Page 31
 1.5 OPTIONS......Page 33
 1.6 TYPES OF TRADERS......Page 36
 1.7 HEDGERS......Page 37
 1.8 SPECULATORS......Page 39
 1.9 ARBITRAGEURS......Page 41
 1.10 OVERVIEW OF THE INDIAN DERIVATIVES MARKET......Page 42
 1.11 DANGERS......Page 50
 SUMMARY......Page 52
 Practice Questions......Page 53
 Further Questions......Page 55
 2.1 BACKGROUND......Page 57
 2.2 SPECIFICATION OF A FUTURES CONTRACT......Page 62
 2.4 THE OPERATION OF MARGIN ACCOUNTS......Page 67
 2.5 OTC MARKETS......Page 71
 2.6 NEWSPAPER QUOTES......Page 74
 2.7 DELIVERY......Page 76
 2.8 TYPES OF TRADERS AND TYPES OF ORDERS......Page 78
 2.9 REGULATION......Page 79
 2.10 ACCOUNTING AND TAX......Page 80
 2.11 FORWARD vs. FUTURES CONTRACTS......Page 82
 SUMMARY......Page 83
 FURTHER READING......Page 84
 Practice Questions......Page 85
 Further Questions......Page 86
 3.1 BASIC PRINCIPLES......Page 89
 3.2 ARGUMENTS FOR AND AGAINST HEDGING......Page 91
 3.3 BASIS RISK......Page 94
 3.4 CROSS HEDGING......Page 98
 3.5 STOCK INDEX FUTURES......Page 102
 3.6 STACK AND ROLL......Page 109
 SUMMARY......Page 111
 FURTHER READING......Page 112
 Practice Questions......Page 113
 Further Questions......Page 114
 APPENDIX : CAPITAL ASSET PRICING MODEL......Page 117
 4.1 TYPES OF RATES......Page 119
 4.2 SWAP RATES......Page 124
 4.3 THE RISK-FREE RATE......Page 125
 4.4 MEASURING INTEREST RATES......Page 126
 4.6 BOND PRICING......Page 129
 4.7 DETERMINING ZERO RATES......Page 131
 4.8 FORWARD RATES......Page 134
 4.9 FORWARD RATE AGREEMENTS......Page 136
 4.10 DURATION......Page 139
 4.11 CONVEXITY......Page 143
 4.12 THEORIES OF THE TERM STRUCTURE OF INTEREST RATES......Page 144
 SUMMARY......Page 146
 Practice Questions......Page 148
 Further Questions......Page 150
 5.1 INVESTMENT ASSETS vs. CONSUMPTION ASSETS......Page 153
 5.2 SHORT SELLING......Page 154
 5.3 ASSUMPTIONS AND NOTATION......Page 155
 5.4 FORWARD PRICE FOR AN INVESTMENT ASSET......Page 156
 5.5 KNOWN INCOME......Page 160
 5.7 VALUING FORWARD CONTRACTS......Page 162
 5.8 ARE FORWARD PRICES AND FUTURES PRICES EQUAL?......Page 165
 5.9 FUTURES PRICES OF STOCK INDICES......Page 166
 5.10 FORWARD AND FUTURES CONTRACTS ON CURRENCIES......Page 167
 5.11 FUTURES ON COMMODITIES......Page 171
 5.12 THE COST OF CARRY......Page 174
 5.14 FUTURES PRICES AND EXPECTED FUTURE SPOT PRICES......Page 175
 SUMMARY......Page 178
 Practice Questions......Page 179
 Further Questions......Page 181
 6.1 DAY COUNT AND QUOTATION CONVENTIONS......Page 183
 6.2 TREASURY BOND FUTURES......Page 186
 6.3 EURODOLLAR FUTURES......Page 192
 6.4 DURATION-BASED HEDGING STRATEGIES USING FUTURES......Page 198
 6.5 HEDGING PORTFOLIOS OF ASSETS AND LIABILITIES......Page 199
 SUMMARY......Page 200
 Practice Questions......Page 201
 Further Questions......Page 203
Chapter 7 - Swaps......Page 205
 7.1 MECHANICS OF INTEREST RATE SWAPS......Page 208
 7.2 DAY COUNT ISSUES......Page 213
 7.3 CONFIRMATIONS......Page 214
 7.4 THE COMPARATIVE-ADVANTAGE ARGUMENT......Page 215
 7.5 VALUATION OF INTEREST RATE SWAPS......Page 219
 7.6 HOW THE VALUE CHANGES THROUGH TIME......Page 221
 7.7 FIXED-FOR-FIXED CURRENCY SWAPS......Page 222
 7.8 VALUATION OF FIXED-FOR-FIXED CURRENCY SWAPS......Page 225
 7.9 OTHER CURRENCY SWAPS......Page 227
 7.10 CREDIT RISK......Page 228
 7.12 OTHER TYPES OF SWAPS......Page 229
 SUMMARY......Page 231
 Practice Questions......Page 232
 Further Questions......Page 235
 8.1 SECURITIZATION......Page 237
 8.2 THE U.S. HOUSING MARKET......Page 241
 8.3 WHAT WENT WRONG?......Page 245
 8.4 THE AFTERMATH......Page 247
 8.5 IMPACT OF THE CRISIS IN INDIA......Page 248
 SUMMARY......Page 249
 Practice Questions......Page 250
 Further Questions......Page 251
 9.1 CVA AND DVA......Page 252
 9.2 FVA AND MVA......Page 255
 9.3 KVA......Page 258
 9.4 CALCULATION ISSUES......Page 259
 FURTHER READING......Page 260
 Further Questions......Page 261
 10.1 TYPES OF OPTIONS......Page 262
 10.2 OPTION POSITIONS......Page 264
 10.3 UNDERLYING ASSETS......Page 267
 10.4 SPECIFICATION OF STOCK OPTIONS......Page 268
 10.5 TRADING......Page 272
 10.6 COMMISSIONS......Page 274
 10.7 MARGIN REQUIREMENTS......Page 275
 10.8 THE OPTIONS CLEARING CORPORATION......Page 277
 10.10 TAXATION......Page 278
 10.11 WARRANTS, EMPLOYEE STOCK OPTIONS, AND CONVERTIBLES......Page 279
 10.12 OVER-THE-COUNTER OPTIONS MARKETS......Page 280
 SUMMARY......Page 281
 Practice Questions......Page 282
 Further Questions......Page 284
 11.1 FACTORS AFFECTING OPTION PRICES......Page 286
 11.2 ASSUMPTIONS AND NOTATION......Page 290
 11.3 UPPER AND LOWER BOUNDS FOR OPTION PRICES......Page 291
 11.4 PUT–CALL PARITY......Page 293
 11.5 CALLS ON A NON-DIVIDEND-PAYING STOCK......Page 296
 11.6 PUTS ON A NON-DIVIDEND-PAYING STOCK......Page 299
 11.7 EFFECT OF DIVIDENDS......Page 301
 SUMMARY......Page 302
 Practice Questions......Page 303
 Further Questions......Page 305
 12.1 PRINCIPAL-PROTECTED NOTES......Page 307
 12.2 TRADING AN OPTION AND THE UNDERLYING ASSET......Page 309
 12.3 SPREADS......Page 311
 12.4 COMBINATIONS......Page 319
 12.5 OTHER PAYOFFS......Page 322
 SUMMARY......Page 323
 Practice Questions......Page 324
 Further Questions......Page 325
 13.1 A ONE-STEP BINOMIAL MODEL AND A NO-ARBITRAGE ARGUMENT......Page 327
 13.2 RISK-NEUTRAL VALUATION......Page 331
 13.3 TWO-STEP BINOMIAL TREES......Page 333
 13.4 A PUT EXAMPLE......Page 336
 13.5 AMERICAN OPTIONS......Page 337
 13.6 DELTA......Page 338
 13.7 MATCHING VOLATILITY WITH u AND d......Page 339
 13.9 INCREASING THE NUMBER OF STEPS......Page 341
 13.10 USING DerivaGem......Page 342
 13.11 OPTIONS ON OTHER ASSETS......Page 343
 SUMMARY......Page 346
 FURTHER READING......Page 347
 Practice Questions......Page 348
 Further Questions......Page 349
 APPENDIX : DERIVATION OF THE BLACK–SCHOLES–MERTON OPTION-PRICING FORMULA FROM A BINOMIAL TREE......Page 351
 14.1 THE MARKOV PROPERTY......Page 355
 14.2 CONTINUOUS-TIME STOCHASTIC PROCESSES......Page 356
 14.3 THE PROCESS FOR A STOCK PRICE......Page 361
 14.4 THE PARAMETERS......Page 364
 14.5 CORRELATED PROCESSES......Page 365
 14.6 ITO ’S LEMMA......Page 366
 14.7 THE LOGNORMAL PROPERTY......Page 367
 SUMMARY......Page 368
 Practice Questions......Page 369
 Further Questions......Page 370
 APPENDIX : A NONRIGOROUS DERIVATION OF ITO  ’S LEMMA......Page 372
Chapter 15 - The Black–Scholes–Merton Model......Page 374
 15.1 LOGNORMAL PROPERTY OF STOCK PRICES......Page 375
 15.2 THE DISTRIBUTION OF THE RATE OF RETURN......Page 376
 15.3 THE EXPECTED RETURN......Page 377
 15.4 VOLATILITY......Page 378
 15.5 THE IDEA UNDERLYING THE BLACK–SCHOLES–MERTON DIFFERENTIAL EQUATION......Page 382
 15.6 DERIVATION OF THE BLACK–SCHOLES–MERTON DIFFERENTIAL EQUATION......Page 384
 15.7 RISK-NEUTRAL VALUATION......Page 387
 15.8 BLACK–SCHOLES–MERTON PRICING FORMULAS......Page 388
 15.9 CUMULATIVE NORMAL DISTRIBUTION FUNCTION......Page 391
 15.10 WARRANTS AND EMPLOYEE STOCK OPTIONS......Page 392
 15.11 IMPLIED VOLATILITIES......Page 394
 15.12 DIVIDENDS......Page 396
 SUMMARY......Page 399
 FURTHER READING......Page 400
 Practice Questions......Page 401
 Further Questions......Page 403
 APPENDIX : PROOF OF THE BLACK–SCHOLES–MERTON FORMULA USING RISK-NEUTRAL VALUATION......Page 405
 16.1 CONTRACTUAL ARRANGEMENTS......Page 408
 16.2 DO OPTIONS ALIGN THE INTERESTS OF SHAREHOLDERS AND MANAGERS?......Page 410
 16.3 ACCOUNTING ISSUES......Page 411
 16.4 VALUATION......Page 412
 16.5 BACKDATING SCANDALS......Page 417
 Practice Questions......Page 418
 Further Questions......Page 419
 17.1 OPTIONS ON STOCK INDICES......Page 421
 17.2 CURRENCY OPTIONS......Page 423
 17.3 OPTIONS ON STOCKS PAYING KNOWN DIVIDEND YIELDS......Page 426
 17.4 VALUATION OF EUROPEAN STOCK INDEX OPTIONS......Page 428
 17.5 VALUATION OF EUROPEAN CURRENCY OPTIONS......Page 431
 17.6 AMERICAN OPTIONS......Page 432
 FURTHER READING......Page 433
 Practice Questions......Page 434
 Further Questions......Page 436
 18.1 NATURE OF FUTURES OPTIONS......Page 437
 18.3 EUROPEAN SPOT AND FUTURES OPTIONS......Page 440
 18.4 PUT–CALL PARITY......Page 441
 18.5 BOUNDS FOR FUTURES OPTIONS......Page 442
 18.6 DRIFT OF A FUTURES PRICE IN A RISK-NEUTRAL WORLD......Page 443
 18.7 BLACK’S MODEL FOR VALUING FUTURES OPTIONS......Page 444
 18.8 USING BLACK’S MODEL INSTEAD OF BLACK–SCHOLES–MERTON......Page 445
 18.9 VALUATION OF FUTURES OPTIONS USING BINOMIAL TREES......Page 446
 18.10 AMERICAN FUTURES OPTIONS vs. AMERICAN SPOT OPTIONS......Page 448
 SUMMARY......Page 449
 Practice Questions......Page 450
 Further Questions......Page 452
 19.1 ILLUSTRATION......Page 453
 19.2 NAKED AND COVERED POSITIONS......Page 454
 19.3 GREEK LETTER CALCULATION......Page 456
 19.4 DELTA HEDGING......Page 457
 19.5 THETA......Page 463
 19.6 GAMMA......Page 465
 19.7 RELATIONSHIP BETWEEN DELTA, THETA, AND GAMMA......Page 469
 19.8 VEGA......Page 470
 19.9 RHO......Page 472
 19.11 THE REALITIES OF HEDGING......Page 473
 19.12 SCENARIO ANALYSIS......Page 474
 19.13 EXTENSION OF FORMULAS......Page 475
 19.14 PORTFOLIO INSURANCE......Page 477
 19.15 STOCK MARKET VOLATILITY......Page 479
 SUMMARY......Page 480
 Practice Questions......Page 482
 APPENDIX : TAYLOR SERIES EXPANSIONS AND GREEK LETTERS......Page 486
 20.1 WHY THE VOLATILITY SMILE IS THE SAME FOR CALLS AND PUTS......Page 487
 20.2 FOREIGN CURRENCY OPTIONS......Page 489
 20.3 EQUITY OPTIONS......Page 492
 20.5 THE VOLATILITY TERM STRUCTURE AND VOLATILITY SURFACES......Page 494
 20.7 THE ROLE OF THE MODEL......Page 496
 20.8 WHEN A SINGLE LARGE JUMP IS ANTICIPATED......Page 497
 SUMMARY......Page 498
 FURTHER READING......Page 499
 Practice Questions......Page 500
 Further Questions......Page 501
 APPENDIX : DETERMINING IMPLIED RISK-NEUTRAL DISTRIBUTIONS FROM VOLATILITY SMILES......Page 503
 21.1 BINOMIAL TREES......Page 506
 21.2 USING THE BINOMIAL TREE FOR OPTIONS ON INDICES, CURRENCIES, AND FUTURES CONTRACTS......Page 514
 21.3 BINOMIAL MODEL FOR A DIVIDEND-PAYING STOCK......Page 516
 21.4 ALTERNATIVE PROCEDURES FOR CONSTRUCTING TREES......Page 521
 21.5 TIME-DEPENDENT PARAMETERS......Page 524
 21.6 MONTE CARLO SIMULATION......Page 525
 21.7 VARIANCE REDUCTION PROCEDURES......Page 531
 21.8 FINITE DIFFERENCE METHODS......Page 534
 SUMMARY......Page 544
 FURTHER READING......Page 545
 Practice Questions......Page 546
 Further Questions......Page 548
Chapter 22 - Value at Risk and Expected Shortfall......Page 550
 22.1 THE VaR AND ES MEASURES......Page 551
 22.2 HISTORICAL SIMULATION......Page 552
 22.3 MODEL-BUILDING APPROACH......Page 558
 22.4 THE LINEAR MODEL......Page 561
 22.5 THE QUADRATIC MODEL......Page 566
 22.6 MONTE CARLO SIMULATION......Page 569
 22.9 PRINCIPAL COMPONENTS ANALYSIS......Page 570
 SUMMARY......Page 574
 FURTHER READING......Page 575
 Practice Questions......Page 576
 Further Questions......Page 577
 23.1 ESTIMATING VOLATILITY......Page 579
 23.2 THE EXPONENTIALLY WEIGHTED MOVING AVERAGE MODEL......Page 581
 23.3 THE GARCH(1,1) MODEL......Page 583
 23.4 CHOOSING BETWEEN THE MODELS......Page 584
 23.5 MAXIMUM LIKELIHOOD METHODS......Page 585
 23.6 USING GARCH(1,1) TO FORECAST FUTURE VOLATILITY......Page 590
 23.7 CORRELATIONS......Page 593
 23.8 APPLICATION OF EWMA TO FOUR-INDEX EXAMPLE......Page 596
 Practice Questions......Page 598
 Further Questions......Page 600
 24.1 CREDIT RATINGS......Page 602
 24.2 HISTORICAL DEFAULT PROBABILITIES......Page 603
 24.3 RECOVERY RATES......Page 604
 24.4 ESTIMATING DEFAULT PROBABILITIES FROM BOND YIELD SPREADS......Page 605
 24.5 COMPARISON OF DEFAULT PROBABILITY ESTIMATES......Page 608
 24.6 USING EQUITY PRICES TO ESTIMATE DEFAULT PROBABILITIES......Page 611
 24.7 CREDIT RISK IN DERIVATIVES TRANSACTIONS......Page 613
 24.8 DEFAULT CORRELATION......Page 619
 24.9 CREDIT VaR......Page 622
 SUMMARY......Page 625
 Practice Questions......Page 626
 Further Questions......Page 628
Chapter 25 - Credit Derivatives......Page 630
 25.1 CREDIT DEFAULT SWAPS......Page 631
 25.2 VALUATION OF CREDIT DEFAULT SWAPS......Page 635
 25.3 CREDIT INDICES......Page 638
 25.4 THE USE OF FIXED COUPONS......Page 639
 25.5 CDS FORWARDS AND OPTIONS......Page 640
 25.7 TOTAL RETURN SWAPS......Page 641
 25.8 COLLATERALIZED DEBT OBLIGATIONS......Page 642
 25.9 ROLE OF CORRELATION IN A BASKET CDS AND CDO......Page 644
 25.10 VALUATION OF A SYNTHETIC CDO......Page 645
 25.11 ALTERNATIVES TO THE STANDARD MARKET MODEL......Page 652
 FURTHER READING......Page 654
 Practice Questions......Page 655
 Further Questions......Page 656
 26.1 PACKAGES......Page 658
 26.2 PERPETUAL AMERICAN CALL AND PUT OPTIONS......Page 659
 26.3 NONSTANDARD AMERICAN OPTIONS......Page 660
 26.4 GAP OPTIONS......Page 661
 26.7 COMPOUND OPTIONS......Page 662
 26.8 CHOOSER OPTIONS......Page 663
 26.9 BARRIER OPTIONS......Page 664
 26.10 BINARY OPTIONS......Page 666
 26.11 LOOKBACK OPTIONS......Page 667
 26.12 SHOUT OPTIONS......Page 669
 26.13 ASIAN OPTIONS......Page 670
 26.14 OPTIONS TO EXCHANGE ONE ASSET FOR ANOTHER......Page 671
 26.15 OPTIONS INVOLVING SEVERAL ASSETS......Page 672
 26.16 VOLATILITY AND VARIANCE SWAPS......Page 673
 26.17 STATIC OPTIONS REPLICATION......Page 677
 FURTHER READING......Page 680
 Practice Questions......Page 681
 Further Questions......Page 683
Chapter 27 - More on Models and Numerical Procedures......Page 685
 27.1 ALTERNATIVES TO BLACK–SCHOLES–MERTON......Page 686
 27.2 STOCHASTIC VOLATILITY MODELS......Page 691
 27.3 THE IVF MODEL......Page 693
 27.4 CONVERTIBLE BONDS......Page 695
 27.5 PATH-DEPENDENT DERIVATIVES......Page 697
 27.6 BARRIER OPTIONS......Page 700
 27.7 OPTIONS ON TWO CORRELATED ASSETS......Page 703
 27.8 MONTE CARLO SIMULATION AND AMERICAN OPTIONS......Page 705
 SUMMARY......Page 709
 FURTHER READING......Page 710
 Practice Questions......Page 711
 Further Questions......Page 713
Chapter 28 - Martingales and Measures......Page 715
 28.1 THE MARKET PRICE OF RISK......Page 716
 28.2 SEVERAL STATE VARIABLES......Page 719
 28.3 MARTINGALES......Page 720
 28.4 ALTERNATIVE CHOICES FOR THE NUMERAIRE......Page 721
 28.5 EXTENSION TO SEVERAL FACTORS......Page 724
 28.6 BLACK’S MODEL REVISITED......Page 725
 28.7 OPTION TO EXCHANGE ONE ASSET FOR ANOTHER......Page 726
 28.8 CHANGE OF NUMERAIRE......Page 727
 SUMMARY......Page 729
 Practice Questions......Page 730
 Further Questions......Page 731
 29.1 BOND OPTIONS......Page 733
 29.2 INTEREST RATE CAPS AND FLOORS......Page 738
 29.3 EUROPEAN SWAP OPTIONS......Page 744
 29.4 HEDGING INTEREST RATE DERIVATIVES......Page 748
 SUMMARY......Page 749
 Practice Questions......Page 750
 Further Questions......Page 751
 30.1 CONVEXITY ADJUSTMENTS......Page 753
 30.2 TIMING ADJUSTMENTS......Page 757
 30.3 QUANTOS......Page 759
 Practice Questions......Page 762
 Further Questions......Page 764
 APPENDIX : PROOF OF THE CONVEXITY ADJUSTMENT FORMULA......Page 765
 31.1 BACKGROUND......Page 766
 31.2 ONE-FACTOR MODELS......Page 768
 31.3 REAL-WORLD VS. RISK-NEUTRAL PROCESSES......Page 773
 31.4 ESTIMATING PARAMETERS......Page 774
 31.5 MORE SOPHISTICATED MODELS......Page 775
 Practice Questions......Page 776
 Further Questions......Page 777
 32.1 EXTENSIONS OF EQUILIBRIUM MODELS......Page 779
 32.2 OPTIONS ON BONDS......Page 783
 32.3 VOLATILITY STRUCTURES......Page 784
 32.4 INTEREST RATE TREES......Page 785
 32.5 A GENERAL TREE-BUILDING PROCEDURE......Page 787
 32.6 CALIBRATION......Page 796
 32.7 HEDGING USING A ONE-FACTOR MODEL......Page 798
 Practice Questions......Page 799
 Further Questions......Page 800
 33.1 THE HEATH, JARROW, AND MORTON MODEL......Page 802
 33.2 THE LIBOR MARKET MODEL......Page 805
 33.3 HANDLING MULTIPLE ZERO CURVES......Page 815
 33.4 AGENCY MORTGAGE-BACKED SECURITIES......Page 816
 SUMMARY......Page 818
 Practice Questions......Page 819
 Further Questions......Page 820
 34.1 VARIATIONS ON THE VANILLA DEAL......Page 821
 34.2 COMPOUNDING SWAPS......Page 823
 34.3 CURRENCY SWAPS......Page 824
 34.4 MORE COMPLEX SWAPS......Page 825
 34.5 EQUITY SWAPS......Page 828
 34.6 SWAPS WITH EMBEDDED OPTIONS......Page 829
 34.7 OTHER SWAPS......Page 832
 SUMMARY......Page 833
 Further Questions......Page 834
Chapter 35 - Energy and Commodity Derivatives......Page 836
 35.2 METALS......Page 837
 35.3 ENERGY PRODUCTS......Page 838
 35.4 MODELING COMMODITY PRICES......Page 840
 35.5 WEATHER DERIVATIVES......Page 846
 35.6 INSURANCE DERIVATIVES......Page 847
 35.7 PRICING WEATHER AND INSURANCE DERIVATIVES......Page 849
 35.8 HOW AN ENERGY PRODUCER CAN HEDGE RISKS......Page 850
 FURTHER READING......Page 851
 Practice Questions......Page 852
 Further Questions......Page 853
 36.1 CAPITAL INVESTMENT APPRAISAL......Page 854
 36.2 EXTENSION OF THE RISK-NEUTRAL VALUATION FRAMEWORK......Page 855
 36.3 ESTIMATING THE MARKET PRICE OF RISK......Page 857
 36.5 EVALUATING OPTIONS IN AN INVESTMENT OPPORTUNITY......Page 858
 FURTHER READING......Page 865
 Further Questions......Page 866
 37.1 LESSONS FOR ALL USERS OF DERIVATIVES......Page 868
 37.2 LESSONS FOR FINANCIAL INSTITUTIONS......Page 872
 37.3 LESSONS FOR NONFINANCIAL CORPORATIONS......Page 879
 FURTHER READING......Page 881
Glossary of Terms......Page 882
DerivaGem Software......Page 905
Major Exchanges Trading Futures and Options......Page 910
Table for N (x) When x  ≤ 0......Page 911
Author Index......Page 914
Subject Index......Page 918