Options, futures, and other derivatives [Ninth edition] 9789332559417, 9789332586567, 9332559414

Table of contents :
Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Detication Page......Page 4
CONTENTS IN BRIEF......Page 5
Contents......Page 6
BUSINESS SNAPSHOTS......Page 17
TECHNICAL NOTES......Page 19
What’s New in the Ninth Edition?......Page 20
Acknowledgments......Page 21
Chapter 1: Introduction......Page 24
1.1 EXCHANGE-TRADED MARKETS......Page 25
1.2 OVER-THE-COUNTER MARKETS......Page 26
Market Size......Page 27
1.3 FORWARD CONTRACTS......Page 29
Payoffs from Forward Contracts......Page 30
1.5 OPTIONS......Page 31
1.6 TYPES OF TRADERS......Page 34
1.7 HEDGERS......Page 35
Hedging Using Options......Page 36
Speculation Using Futures......Page 37
Speculation Using Options......Page 38
1.10 OVERVIEW OF THE INDIAN DERIVATIVES MARKET......Page 40
Exchange-Traded Markets......Page 41
years now.Swaps......Page 43
Derivatives in the Asia-Pacific Region......Page 44
1.11 DANGERS......Page 48
SUMMARY......Page 49
Practice Questions (Answers in Solutions Manual)......Page 50
Further Questions......Page 52
2.1 BACKGROUND......Page 54
Closing Out Positions......Page 56
The Asset......Page 59
Delivery Arrangements......Page 60
Equity Markets......Page 61
Currency Futures......Page 62
2.4 THE OPERATION OF MARGIN ACCOUNTS......Page 64
Daily Settlement......Page 65
The Clearing House and Its Members......Page 67
2.5 OTC MARKETS......Page 68
Bilateral Clearing......Page 69
2.6 NEWSPAPER QUOTES......Page 71
Open Interest......Page 72
2.7 DELIVERY......Page 74
Orders......Page 75
2.9 REGULATION......Page 76
Accounting......Page 77
Tax......Page 78
Profits from Forward and Futures Contracts......Page 79
Indian Regulators......Page 80
SUMMARY......Page 81
Practice Questions (Answers in Solutions Manual)......Page 82
Further Questions......Page 84
3.1 BASIC PRINCIPLES......Page 86
Long Hedges......Page 87
3.2 ARGUMENTS FOR AND AGAINST HEDGING......Page 88
Hedging and Competitors......Page 89
Hedging Can Lead to a Worse Outcome......Page 90
The Basis......Page 92
Choice of Contract......Page 94
3.4 CROSS HEDGING......Page 95
Calculating the Minimum Variance Hedge Ratio......Page 96
Optimal Number of Contracts......Page 97
3.5 STOCK INDEX FUTURES......Page 99
Stock Indices......Page 100
Hedging an Equity Portfolio......Page 101
Reasons for Hedging an Equity Portfolio......Page 103
Locking in the Benefits of Stock Picking......Page 104
3.6 STACK AND ROLL......Page 105
SUMMARY......Page 107
FURTHER READING......Page 108
Practice Questions (Answers in Solutions Manual......Page 109
Further Questions......Page 111
APPENDIXCAPITAL ASSET PRICING MODEL......Page 113
Treasury Rates......Page 115
LIBOR......Page 116
The Fed Funds Rate......Page 117
Repo and Reverse Repo Rates in India......Page 118
Collaterized Borrowing and Lending Obligation (CBLO)......Page 119
4.2 MEASURING INTEREST RATES......Page 120
Continuous Compounding......Page 122
4.4 BOND PRICING......Page 123
Par Yield......Page 124
4.5 DETERMINING TREASURY ZERO RATES......Page 125
4.6 FORWARD RATES......Page 127
4.7 FORWARD RATE AGREEMENTS......Page 129
Valuation......Page 131
4.8 DURATION......Page 133
Modified Duration......Page 135
Bond Portfolios......Page 136
4.9 CONVEXITY......Page 137
The Management of Net Interest Income......Page 138
Liquidity......Page 140
FURTHER READING......Page 141
Practice Questions......Page 142
Further Questions......Page 144
5.1 INVESTMENT ASSETS vs. CONSUMPTION ASSETS......Page 146
5.2 SHORT SELLING......Page 147
5.3 ASSUMPTIONS AND NOTATION......Page 148
A Generalization......Page 149
What If Short Sales Are Not Possible?......Page 151
The Securities Lending and Borrowing Mechanism......Page 152
5.5 KNOWN INCOME......Page 153
A Generalization......Page 154
5.6 KNOWN YIELD......Page 155
5.7 VALUING FORWARD CONTRACTS......Page 156
5.8 ARE FORWARD PRICES AND FUTURES PRICES EQUAL?......Page 157
5.9 FUTURES PRICES OF STOCK INDICES......Page 158
5.10 FORWARD AND FUTURES CONTRACTS ON CURRENCIES......Page 161
A Foreign Currency as an Asset Providing a Known Yield......Page 163
Income and Storage Costs......Page 164
Consumption Commodities......Page 165
Convenience Yields......Page 166
5.12 THE COST OF CARRY......Page 167
Keynes and Hicks......Page 168
The Risk in a Futures Position......Page 169
SUMMARY......Page 170
Practice Questions......Page 172
Further Questions......Page 174
Day Counts......Page 176
Price Quotations of US Treasury Bonds......Page 178
6.2 TREASURY BOND FUTURES......Page 179
Conversion Factors......Page 181
Cheapest-to-Deliver Bond......Page 182
Determining the Futures Price......Page 183
6.3 EURODOLLAR FUTURES......Page 185
Forward vs. Futures Interest Rates......Page 187
Convexity Adjustment......Page 188
Using Eurodollar Futures to Extend the LIBOR Zero Curve......Page 189
Product Characteristics and Settlement Mechanism in India......Page 190
6.4 DURATION-BASED HEDGING STRATEGIES USING FUTURES......Page 191
6.5 HEDGING PORTFOLIOS OF ASSETS AND LIABILITIES......Page 192
SUMMARY......Page 193
Practice Questions......Page 194
Further Questions......Page 196
Chapter 7: Swaps......Page 198
History of Swaps in India......Page 199
Illustration......Page 201
Using the Swap to Transform a Liability......Page 203
Using the Swap to Transform an Asset......Page 204
Market Makers......Page 205
7.2 DAY COUNT ISSUES......Page 206
7.3 CONFIRMATIONS......Page 207
7.4 THE COMPARATIVE-ADVANTAGE ARGUMENT......Page 208
Criticism of the Argument......Page 210
7.5 THE NATURE OF SWAP RATES......Page 211
7.7 VALUATION OF INTEREST RATE SWAPS......Page 212
Valuation in Terms of Bond Prices......Page 213
7.9 FIXED-FOR-FIXED CURRENCY SWAPS......Page 216
Illustration......Page 217
Comparative Advantage......Page 218
7.10 VALUATION OF FIXED-FOR-FIXED CURRENCY SWAPS......Page 220
Valuation as Portfolio of Forward Contracts......Page 221
7.11 OTHER CURRENCY SWAPS......Page 223
7.12 CREDIT RISK......Page 224
Variations on the Standard Interest Rate Swap......Page 226
Options......Page 227
SUMMARY......Page 228
Practice Questions......Page 229
Further Questions......Page 231
8.1 SECURITIZATION......Page 233
ABSs......Page 234
ABS CDOs......Page 236
The Relaxation of Lending Standards......Page 237
Subprime Mortgage Securitization......Page 238
The Bubble Bursts......Page 239
The Losses......Page 240
8.3 WHAT WENT WRONG?......Page 241
Incentives......Page 242
8.4 THE AFTERMATH......Page 243
8.5 IMPACT OF THE CRISIS IN INDIA......Page 244
SUMMARY......Page 245
Practice Questions......Page 246
Further Questions......Page 247
9.1 THE RISK-FREE RATE......Page 248
9.2 THE OIS RATE......Page 250
Determining the OIS Zero Curve......Page 252
Determining Forward LIBOR Rates with OIS Discounting......Page 253
9.4 OIS vs. LIBOR: WHICH IS CORRECT?......Page 254
9.5 CREDIT RISK: CVA AND DVA......Page 255
9.6 FUNDING COSTS......Page 257
FURTHER READING......Page 259
Further Questions......Page 260
10.1 TYPES OF OPTIONS......Page 262
Call Options......Page 263
Put Options......Page 264
10.2 OPTION POSITIONS......Page 265
Stock Options......Page 267
Expiration Dates......Page 268
Terminology......Page 269
Other Nonstandard Products......Page 270
Dividends and Stock Splits......Page 271
10.5 TRADING......Page 272
Issues in Options Trading in India......Page 273
10.6 COMMISSIONS......Page 274
Writing Naked Options......Page 275
10.8 THE OPTIONS CLEARING CORPORATION......Page 276
10.10 TAXATION......Page 277
Constructive Sales......Page 278
10.11 WARRANTS, EMPLOYEE STOCK OPTIONS, AND CONVERTIBLES......Page 279
Types of Options Markets Available in India......Page 280
FURTHER READING......Page 281
Practice Questions (Answers in Solutions Manual)......Page 282
Further Questions......Page 283
11.1 FACTORS AFFECTING OPTION PRICES......Page 285
Volatility......Page 286
Amount of Future Dividends......Page 288
Upper Bounds......Page 289
Lower Bound for Calls on Non-Dividend-Paying Stocks......Page 290
Lower Bound for European Puts on Non-Dividend-Paying Stocks......Page 291
11.4 PUT–CALL PARITY......Page 292
American Options......Page 295
11.5 CALLS ON A NON-DIVIDEND-PAYING STOCK......Page 296
11.6 PUTS ON A NON-DIVIDEND-PAYING STOCK......Page 297
Bounds......Page 298
Lower Bound for Calls and Puts......Page 300
SUMMARY......Page 301
Practice Questions (Answers in Solutions Manual)......Page 302
Further Questions......Page 304
12.1 PRINCIPAL-PROTECTED NOTES......Page 305
12.2 TRADING AN OPTION AND THE UNDERLYING ASSET......Page 307
12.3 SPREADS......Page 309
Bear Spreads......Page 311
Butterfly Spreads......Page 313
Calendar Spreads......Page 316
12.4 COMBINATIONS......Page 317
Straddle......Page 318
Strips and Straps......Page 319
12.5 OTHER PAYOFFS......Page 320
SUMMARY......Page 321
Practice Questions (Answers in Solutions Manual)......Page 322
Further Questions......Page 323
13.1 A ONE-STEP BINOMIAL MODEL AND A NO-ARBITRAGE ARGUMENT......Page 325
A Generalization......Page 327
13.2 RISK-NEUTRAL VALUATION......Page 329
The One-Step Binomial Example Revisited......Page 330
13.3 TWO-STEP BINOMIAL TREES......Page 331
A Generalization......Page 333
13.4 A PUT EXAMPLE......Page 334
13.5 AMERICAN OPTIONS......Page 335
13.6 DELTA......Page 336
13.7 MATCHING VOLATILITY WITH u AND d......Page 337
Girsanov’s Theorem......Page 338
13.9 INCREASING THE NUMBER OF STEPS......Page 339
13.10 USING DerivaGem......Page 340
Options on Stocks Paying a Continuous Dividend Yield......Page 341
Options on Stock Indices......Page 342
Options on Currencies......Page 343
SUMMARY......Page 344
FURTHER READING......Page 345
Practice Questions (Answers in Solutions Manual)......Page 346
Further Questions......Page 347
DERIVATION OF THE BLACK–SCHOLES–MERTON OPTION-PRICING FORMULA FROM A BINOMIAL TREE......Page 349
14.1 THE MARKOV PROPERTY......Page 353
14.2 CONTINUOUS-TIME STOCHASTIC PROCESSES......Page 354
Wiener Process......Page 355
Generalized Wiener Process......Page 356
14.3 THE PROCESS FOR A STOCK PRICE......Page 359
Discrete-Time Model......Page 360
Monte Carlo Simulation......Page 361
14.4 THE PARAMETERS......Page 362
14.5 CORRELATED PROCESSES......Page 363
14.6 ITÔ’S LEMMA......Page 364
14.7 THE LOGNORMAL PROPERTY......Page 365
SUMMARY......Page 366
Practice Questions (Answers in Solutions Manual)......Page 367
Further Questions......Page 368
DERIVATION OF ITÔ’S LEMMA......Page 370
Chapter 15: The Black–Scholes–Merton Model......Page 372
15.1 LOGNORMAL PROPERTY OF STOCK PRICES......Page 373
15.2 THE DISTRIBUTION OF THE RATE OF RETURN......Page 374
15.3 THE EXPECTED RETURN......Page 375
15.4 VOLATILITY......Page 376
Estimating Volatility from Historical Data......Page 377
Trading Days vs. Calendar Days......Page 379
15.5 THE IDEA UNDERLYING THE BLACK–SCHOLES–MERTON DIFFERENTIAL EQUATION......Page 380
15.6 DERIVATION OF THE BLACK–SCHOLES–MERTON DIFFERENTIAL EQUATION......Page 382
The Prices of Tradeable Derivatives......Page 384
15.7 RISK-NEUTRAL VALUATION......Page 385
15.8 BLACK–SCHOLES–MERTON PRICING FORMULAS......Page 386
Properties of the Black–Scholes–Merton Formulas......Page 388
15.9 CUMULATIVE NORMAL DISTRIBUTION FUNCTION......Page 389
15.10 WARRANTS AND EMPLOYEE STOCK OPTIONS......Page 390
15.11 IMPLIED VOLATILITIES......Page 392
The VIX Index......Page 393
European Options......Page 394
American Call Options......Page 395
SUMMARY......Page 397
FURTHER READING......Page 398
Practice Questions (Answers in Solutions Manual)......Page 399
Further Questions......Page 401
Proof of Key Result......Page 403
The Black–Scholes–Merton Result......Page 404
16.1 CONTRACTUAL ARRANGEMENTS......Page 405
The Early Exercise Decision......Page 406
16.2 DO OPTIONS ALIGN THE INTERESTS OF SHAREHOLDERS AND MANAGERS?......Page 407
16.3 ACCOUNTING ISSUES......Page 408
16.4 VALUATION......Page 409
Binomial Tree Approach......Page 410
The Exercise Multiple Approach......Page 412
Dilution......Page 413
16.5 BACKDATING SCANDALS......Page 414
SUMMARY......Page 415
Practice Questions (Answers in Solutions Manual)......Page 416
Further Questions......Page 417
Portfolio Insurance......Page 418
When the Portfolio’s Beta Is Not 1.0......Page 419
17.2 CURRENCY OPTIONS......Page 420
Range Forwards......Page 421
Lower Bounds for Option Prices......Page 423
Pricing Formulas......Page 424
17.4 VALUATION OF EUROPEAN STOCK INDEX OPTIONS......Page 425
Forward Prices......Page 426
Implied Dividend Yields......Page 427
17.5 VALUATION OF EUROPEAN CURRENCY OPTIONS......Page 428
17.6 AMERICAN OPTIONS......Page 429
FURTHER READING......Page 430
Practice Questions (Answers in Solutions Manual)......Page 431
Further Questions......Page 433
18.1 NATURE OF FUTURES OPTIONS......Page 434
Expiration Months......Page 435
Options on Interest Rate Futures......Page 436
18.3 EUROPEAN SPOT AND FUTURES OPTIONS......Page 437
18.4 PUT–CALL PARITY......Page 438
18.5 BOUNDS FOR FUTURES OPTIONS......Page 439
18.6 VALUATION OF FUTURES OPTIONS USING BINOMIAL TREES......Page 440
A Generalization......Page 441
18.7 DRIFT OF A FUTURES PRICE IN A RISK-NEUTRAL WORLD......Page 442
18.8 BLACK’S MODEL FOR VALUING FUTURES OPTIONS......Page 443
Using Black’s Model Instead of Black–Scholes–Merton......Page 444
18.10 FUTURES-STYLE OPTIONS......Page 445
SUMMARY......Page 446
Practice Questions (Answers in Solutions Manual)......Page 447
Further Questions......Page 448
19.1 ILLUSTRATION......Page 450
19.3 A STOP-LOSS STRATEGY......Page 451
19.4 DELTA HEDGING......Page 453
Delta of European Stock Options......Page 455
Dynamic Aspects of Delta Hedging......Page 456
Delta of a Portfolio......Page 459
19.5 THETA......Page 460
19.6 GAMMA......Page 462
Making a Portfolio Gamma Neutral......Page 464
Calculation of Gamma......Page 465
19.8 VEGA......Page 466
19.9 RHO......Page 468
19.10 THE REALITIES OF HEDGING......Page 469
19.11 SCENARIO ANALYSIS......Page 470
Delta of Forward Contracts......Page 471
Delta of a Futures Contract......Page 472
19.13 PORTFOLIO INSURANCE......Page 473
Use of Index Futures......Page 474
19.14 STOCK MARKET VOLATILITY......Page 475
SUMMARY......Page 476
Practice Questions (Answers in Solutions Manual)......Page 477
Further Questions......Page 479
TAYLOR SERIES EXPANSIONS AND HEDGE PARAMETERS......Page 481
20.1 WHY THE VOLATILITY SMILE IS THE SAME FOR CALLS AND PUTS......Page 482
20.2 FOREIGN CURRENCY OPTIONS......Page 484
Empirical Results......Page 485
Reasons for the Smile in Foreign Currency Options......Page 486
20.3 EQUITY OPTIONS......Page 487
20.4 ALTERNATIVE WAYS OF CHARACTERIZING THE VOLATILITY SMILE......Page 488
20.5 THE VOLATILITY TERM STRUCTURE AND VOLATILITY SURFACES......Page 489
20.6 GREEK LETTERS......Page 490
20.8 WHEN A SINGLE LARGE JUMP IS ANTICIPATED......Page 491
SUMMARY......Page 493
Practice Questions (Answers in Solutions Manual)......Page 494
Further Questions......Page 496
DETERMINING IMPLIED RISK-NEUTRAL DISTRIBUTIONS FROM VOLATILITY SMILES......Page 498
21.1 BINOMIAL TREES......Page 501
Determination of p, u, and d......Page 502
Working Backward through the Tree......Page 503
Expressing the Approach Algebraically......Page 506
Estimating Delta and Other Greek Letters......Page 507
21.2 USING THE BINOMIAL TREE FOR OPTIONS ON INDICES, CURRENCIES, AND FUTURES CONTRACTS......Page 509
Known Dividend Yield......Page 511
Known Dollar Dividend......Page 512
Control Variate Technique......Page 514
21.4 ALTERNATIVE PROCEDURES FOR CONSTRUCTING TREES......Page 516
Trinomial Trees......Page 518
21.5 TIME-DEPENDENT PARAMETERS......Page 519
21.6 MONTE CARLO SIMULATION......Page 520
Derivatives Dependent on More than One Market Variable......Page 522
Number of Trials......Page 524
Sampling through a Tree......Page 525
Applications......Page 526
Control Variate Technique......Page 527
Moment Matching......Page 528
21.8 FINITE DIFFERENCE METHODS......Page 529
Implicit Finite Difference Method......Page 530
Explicit Finite Difference Method......Page 533
Change of Variable......Page 535
Relation to Trinomial Tree Approaches......Page 537
Applications of Finite Difference Methods......Page 539
FURTHER READING......Page 540
Practice Questions (Answers in Solutions Manual)......Page 541
Further Questions......Page 543
Chapter 22: Value at Risk......Page 545
22.1 THE VaR MEASURE......Page 546
22.2 HISTORICAL SIMULATION......Page 548
Illustration: Investment in Four Stock Indices......Page 549
Daily Volatilities......Page 552
Single-Asset Case......Page 553
Two-Asset Case......Page 554
22.4 THE LINEAR MODEL......Page 555
Correlation and Covariance Matrices......Page 556
Handling Interest Rates......Page 557
The Linear Model and Options......Page 558
22.5 THE QUADRATIC MODEL......Page 560
22.7 COMPARISON OF APPROACHES......Page 563
22.8 STRESS TESTING AND BACK TESTING......Page 564
22.9 PRINCIPAL COMPONENTS ANALYSIS......Page 565
Using Principal Components Analysis to Calculate VaR......Page 566
Popular Methods of VaR as Used in the Indian Context......Page 568
FURTHER READING......Page 569
Practice Questions (Answers in Solutions Manual)......Page 570
Further Questions......Page 571
23.1 ESTIMATING VOLATILITY......Page 573
Weighting Schemes......Page 574
23.2 THE EXPONENTIALLY WEIGHTED MOVING AVERAGE MODEL......Page 575
23.3 THE GARCH(1,1) MODEL......Page 577
23.4 CHOOSING BETWEEN THE MODELS......Page 578
Estimating a Constant Variance......Page 579
Estimating EWMA or GARCH (1,1) Parameters......Page 580
How Good Is the Model?......Page 583
23.6 USING GARCH(1,1) TO FORECAST FUTURE VOLATILITY......Page 584
Volatility Term Structures......Page 585
Impact of Volatility Changes......Page 586
23.7 CORRELATIONS......Page 587
Consistency Condition for Covariances......Page 589
23.8 APPLICATION OF EWMA TO FOUR-INDEX EXAMPLE......Page 590
Practice Questions (Answers in Solutions Manual)......Page 592
Further Questions......Page 594
24.1 CREDIT RATINGS......Page 596
Hazard Rates......Page 597
24.3 RECOVERY RATES......Page 598
24.4 ESTIMATING DEFAULT PROBABILITIES FROM BOND YIELD SPREADS......Page 599
Matching Bond Prices......Page 600
Asset Swap Spreads......Page 601
24.5 COMPARISON OF DEFAULT PROBABILITY ESTIMATES......Page 602
Real-World vs. Risk-Neutral Probabilities......Page 604
24.6 USING EQUITY PRICES TO ESTIMATE DEFAULT PROBABILITIES......Page 605
CVA and DVA......Page 607
Special Cases......Page 610
24.8 DEFAULT CORRELATION......Page 613
The Gaussian Copula Model for Time to Default......Page 614
A Factor-Based Correlation Structure......Page 615
24.9 CREDIT VaR......Page 616
CreditMetrics......Page 617
Issues Related to Measurement of Credit Risk in India......Page 619
FURTHER READING......Page 620
Practice Questions (Answers in the Solutions Manual)......Page 621
Further Questions......Page 623
Chapter 25: Credit Derivatives......Page 624
25.1 CREDIT DEFAULT SWAPS......Page 625
The Cheapest-to-Deliver Bond......Page 627
25.2 VALUATION OF CREDIT DEFAULT SWAPS......Page 629
Estimating Default Probabilities......Page 631
25.3 CREDIT INDICES......Page 632
25.4 THE USE OF FIXED COUPONS......Page 633
25.5 CDS FORWARDS AND OPTIONS......Page 634
25.7 TOTAL RETURN SWAPS......Page 635
Synthetic CDOs......Page 636
Standard Portfolios and Single-Tranche Trading......Page 637
25.9 ROLE OF CORRELATION IN A BASKET CDS AND CDO......Page 638
25.10 VALUATION OF A SYNTHETIC CDO......Page 639
Using the Gaussian Copula Model of Time to Default......Page 640
Valuation of kth-to-Default CDS......Page 642
Implied Correlation......Page 644
Valuing Nonstandard Tranches......Page 645
Random Factor Loadings......Page 646
Main Players and Popular Credit Derivatives in India......Page 647
FURTHER READING......Page 648
Practice Questions (Answers in Solutions Manual)......Page 649
Further Questions......Page 650
26.1 PACKAGES......Page 652
26.2 PERPETUAL AMERICAN CALL AND PUT OPTIONS......Page 653
26.3 NONSTANDARD AMERICAN OPTIONS......Page 654
26.4 GAP OPTIONS......Page 655
26.7 COMPOUND OPTIONS......Page 656
26.8 CHOOSER OPTIONS......Page 657
26.9 BARRIER OPTIONS......Page 658
26.10 BINARY OPTIONS......Page 660
26.11 LOOKBACK OPTIONS......Page 661
26.13 ASIAN OPTIONS......Page 663
26.14 OPTIONS TO EXCHANGE ONE ASSET FOR ANOTHER......Page 665
26.15 OPTIONS INVOLVING SEVERAL ASSETS......Page 666
Valuation of Variance Swap......Page 667
The VIX Index......Page 669
Popular Exotic Options in India......Page 670
26.17 STATIC OPTIONS REPLICATION......Page 671
Regulatory Position on Exotic Options......Page 673
FURTHER READING......Page 674
Practice Questions (Answers in Solutions Manual)......Page 675
Further Questions......Page 677
Chapter 27: More on Modelsand Numerical Procedures......Page 679
The Constant Elasticity of Variance Model......Page 680
Merton’s Mixed Jump–Diffusion Model......Page 681
The Variance-Gamma Model......Page 683
27.2 STOCHASTIC VOLATILITY MODELS......Page 685
27.3 THE IVF MODEL......Page 687
27.4 CONVERTIBLE BONDS......Page 688
Illustration Using Lookback Options......Page 691
Generalization......Page 693
27.6 BARRIER OPTIONS......Page 695
The Adaptive Mesh Model......Page 697
Transforming Variables......Page 698
Adjusting the Probabilities......Page 700
The Least-Squares Approach......Page 701
The Exercise Boundary Parameterization Approach......Page 704
SUMMARY......Page 705
FURTHER READING......Page 706
Practice Questions (Answers in Solutions Manual)......Page 707
Further Questions......Page 708
Chapter 28: Martingales and Measures......Page 710
28.1 THE MARKET PRICE OF RISK......Page 711
Alternative Worlds......Page 713
28.2 SEVERAL STATE VARIABLES......Page 714
The Equivalent Martingale Measure Result......Page 715
28.4 ALTERNATIVE CHOICES FOR THE NUMERAIRE......Page 716
Zero-Coupon Bond Price as the Numeraire......Page 717
Interest Rates When Zero-Coupon Bond Price is the Numeraire......Page 718
Annuity Factor as the Numeraire......Page 719
28.5 EXTENSION TO SEVERAL FACTORS......Page 720
28.6 BLACK’S MODEL REVISITED......Page 721
28.7 OPTION TO EXCHANGE ONE ASSET FOR ANOTHER......Page 722
28.8 CHANGE OF NUMERAIRE......Page 723
SUMMARY......Page 724
Practice Questions (Answers in the Solutions Manual)......Page 725
Further Questions......Page 727
Embedded Bond Options......Page 728
European Bond Options......Page 729
Yield Volatilities......Page 732
The Cap as a Portfolio of Interest Rate Options......Page 733
Valuation of Caps and Floors......Page 734
Spot Volatilities vs. Flat Volatilities......Page 736
Theoretical Justification for the Model......Page 737
The Impact of Day Count Conventions......Page 738
Valuation of European Swaptions......Page 739
Theoretical Justification for the Swaption Model......Page 742
Some of the Popular Interest Rate Derivatives used in IndianMarkets......Page 743
29.5 HEDGING INTEREST RATE DERIVATIVES......Page 744
SUMMARY......Page 745
Practice Questions (Answers in Solutions Manual)......Page 746
Further Questions......Page 747
30.1 CONVEXITY ADJUSTMENTS......Page 749
Application 1: Interest Rates......Page 751
Application 2: Swap Rates......Page 752
30.2 TIMING ADJUSTMENTS......Page 753
Application 1 Revisited......Page 754
30.3 QUANTOS......Page 755
Using Traditional Risk-Neutral Measures......Page 756
Practice Questions (Answers in Solutions Manual)......Page 758
Further Questions......Page 760
PROOF OF THE CONVEXITY ADJUSTMENT FORMULA......Page 761
31.1 BACKGROUND......Page 762
31.2 EQUILIBRIUM MODELS......Page 763
The Vasicek Model......Page 764
Properties of Vasicek and CIR......Page 766
Applications of Equilibrium Models......Page 769
31.3 NO-ARBITRAGE MODELS......Page 770
The Ho–Lee Model......Page 771
The Hull–White (One-Factor) Model......Page 772
The Black–Karasinski Model......Page 774
31.4 OPTIONS ON BONDS......Page 775
31.5 VOLATILITY STRUCTURES......Page 776
Illustration of Use of Trinomial Trees......Page 777
Nonstandard Branching......Page 778
First Stage......Page 779
Illustration of Second Stage......Page 782
Extension to Other Models......Page 784
Using Analytic Results in Conjunction with Trees......Page 786
31.8 CALIBRATION......Page 788
31.9 HEDGING USING A ONE-FACTOR MODEL......Page 790
FURTHER READING......Page 791
Practice Questions (Answers in Solutions Manual)......Page 792
Further Questions......Page 794
32.1 THE HEATH, JARROW, AND MORTON MODEL......Page 796
Processes for Zero-Coupon Bond Prices and Forward Rates......Page 797
32.2 THE LIBOR MARKET MODEL......Page 799
The Model......Page 800
Forward Rate Volatilities......Page 801
Extension to Several Factors......Page 802
Ratchet Caps, Sticky Caps, and Flexi Caps......Page 803
Valuing European Swap Options......Page 805
Calibrating the Model......Page 807
Bermudan Swap Options......Page 808
32.3 HANDLING MULTIPLE ZERO CURVES......Page 809
32.4 AGENCY MORTGAGE-BACKED SECURITIES......Page 811
Option-Adjusted Spread......Page 812
SUMMARY......Page 813
Practice Questions (Answers in Solutions Manual)......Page 814
Further Questions......Page 815
33.1 VARIATIONS ON THE VANILLA DEAL......Page 816
33.2 COMPOUNDING SWAPS......Page 818
33.3 CURRENCY SWAPS......Page 819
LIBOR-in-Arrears Swap......Page 820
CMS and CMT Swaps......Page 821
33.5 EQUITY SWAPS......Page 823
Accrual Swaps......Page 825
Cancelable Compounding Swaps......Page 826
33.7 OTHER SWAPS......Page 827
SUMMARY......Page 828
Practice Questions (Answers in Solutions Manual)......Page 829
Further Questions......Page 830
Chapter 34: Energy and Commodity Derivatives......Page 831
34.1 AGRICULTURAL COMMODITIES......Page 832
Crude Oil......Page 833
Electricity......Page 834
34.4 MODELING COMMODITY PRICES......Page 835
A Simple Process......Page 836
Mean Reversion......Page 837
Interpolation and Seasonality......Page 839
Jumps......Page 840
34.5 WEATHER DERIVATIVES......Page 841
34.6 INSURANCE DERIVATIVES......Page 843
34.7 PRICING WEATHER AND INSURANCE DERIVATIVES......Page 844
34.8 HOW AN ENERGY PRODUCER CAN HEDGE RISKS......Page 845
FURTHER READING......Page 846
Practice Questions (Answers in Solutions Manual)......Page 847
Further Questions......Page 848
35.1 CAPITAL INVESTMENT APPRAISAL......Page 849
35.2 EXTENSION OF THE RISK-NEUTRAL VALUATION FRAMEWORK......Page 850
35.3 ESTIMATING THE MARKET PRICE OF RISK......Page 852
35.5 EVALUATING OPTIONS IN AN INVESTMENT OPPORTUNITY......Page 853
Use of a Tree......Page 855
Option to Abandon......Page 857
Option to Expand......Page 858
Multiple Options......Page 859
FURTHER READING......Page 860
Further Questions......Page 861
36.1 LESSONS FOR ALL USERS OF DERIVATIVES......Page 863
Define Risk Limits......Page 865
Do Not Assume You Can Outguess the Market......Page 866
Monitor Traders Carefully......Page 867
Be Conservative in Recognizing Inception Profits......Page 868
Do Not Ignore Liquidity Risk......Page 869
Beware When Everyone Is Following the Same Trading Strategy......Page 870
Market Transparency Is Important......Page 871
Lessons for Financial Institutions—Indian Context Be Aware of the Regulatory and Legal Constraints......Page 872
Make Sure a Hedger Does Not Become a Speculator......Page 874
Lessons for Nonfinancial Institutions—Indian Context Monitor the Market Carefully......Page 875
FURTHER READING......Page 876
Glossary of Terms......Page 877
Getting Started......Page 899
Next Steps......Page 900
Bond Options......Page 901
CDOs......Page 902
The Applications Builder......Page 903
Major Exchanges Trading Futures and Options......Page 904
Table for N(x) When x ≤ 0......Page 905
Table for N(x) When x ≥ 0......Page 906
Author Index......Page 907
Subject Index......Page 911