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contents of volume one
Visual Basic Code xxv
Prolog to the Second Edition xxvii
PART ONE MATHEMATICAL AND FINANCIAL FOUNDATIONS; BASIC
THEORY OF DERIVATIVES; RISK AND RETURN 1
1 Products and Markets 5
2 Derivatives 25
3 The Random Behavior of Assets 55
4 Elementary Stochastic Calculus 71
5 The Black–Scholes Model 91
6 Partial Differential Equations 101
7 The Black–Scholes Formulae and the ‘Greeks’ 109
8 Simple Generalizations of the Black–Scholes World 139
9 Early Exercise and American Options 151
10 Probability Density Functions and First-exit Times 169
11 Multi-asset Options 183
12 How to Delta Hedge 197
13 Fixed-income Products and Analysis: Yield, Duration and Convexity 225
14 Swaps 251
viii contents
15 The Binomial Model 261
16 How Accurate is the Normal Approximation? 295
17 Investment Lessons from Blackjack and Gambling 301
18 Portfolio Management 317
19 Value at Risk 331
20 Forecasting the Markets? 343
21 A Trading Game 359
contents ix
contents of volume two
PART TWO EXOTIC CONTRACTS AND PATH DEPENDENCY 365
22 An Introduction to Exotic and Path-dependent Derivatives 367
23 Barrier Options 385
24 Strongly Path-dependent Derivatives 417
25 Asian Options 427
26 Lookback Options 445
27 Derivatives and Stochastic Control 453
28 Miscellaneous Exotics 461
29 Equity and FX Term Sheets 481
PART THREE FIXED-INCOME MODELING AND DERIVATIVES 507
30 One-factor Interest Rate Modeling 509
31 Yield Curve Fitting 525
32 Interest Rate Derivatives 533
33 Convertible Bonds 553
34 Mortgage-backed Securities 571
35 Multi-factor Interest Rate Modeling 581
36 Empirical Behavior of the Spot Interest Rate 595
37 The Heath, Jarrow & Morton and Brace, Gatarek & Musiela Models 609
38 Fixed-income Term Sheets 627
PART FOUR CREDIT RISK 637
39 Value of the Firm and the Risk of Default 639
40 Credit Risk 649
x contents
41 Credit Derivatives 675
42 RiskMetrics and CreditMetrics 701
43 CrashMetrics 709
44 Derivatives **** Ups 731
contents xix
contents of volume three
PART FIVE ADVANCED TOPICS 745
45 Financial Modeling 749
46 Defects in the Black–Scholes Model 755
47 Discrete Hedging 763
48 Transaction Costs 783
49 Overview of Volatility Modeling 813
50 Deterministic Volatility Surfaces 833
51 Stochastic Volatility 853
52 Uncertain Parameters 869
53 Empirical Analysis of Volatility 881
54 Stochastic Volatility and Mean-variance Analysis 889
55 Asymptotic Analysis of Volatility 901
56 Volatility Case Study: The Cliquet Option 915
57 Jump Diffusion 927
58 Crash Modeling 939
59 Speculating with Options 953
60 Static Hedging 969
61 The Feedback Effect of Hedging in Illiquid Markets 989
62 Utility Theory 1005
63 More About American Options and Related Matters 1013
64 Advanced Dividend Modeling 1035
65 Serial Autocorrelation in Returns 1045
66 Asset Allocation in Continuous Time 1051
xx contents
67 Asset Allocation Under Threat of a Crash 1061
68 Interest-rate Modeling Without Probabilities 1077
69 Pricing and Optimal Hedging of Derivatives, the Non-probabilistic
Model Cont’d 1099
70 Extensions to the Non-probabilistic Interest-rate Model 1117
71 Modeling Inflation 1129
72 Energy Derivatives 1141
73 Real Options 1151
74 Life Settlements and Viaticals 1161
75 Bonus Time 1175
PART SIX NUMERICAL METHODS AND PROGRAMS 1189
76 Overview of Numerical Methods 1191
77 Finite-difference Methods for One-factor Models 1199
78 Further Finite-difference Methods for One-factor Models 1227
79 Finite-difference Methods for Two-factor Models 1253
80 Monte Carlo Simulation 1263
81 Numerical Integration 1285
82 Finite-difference Programs 1295
83 Monte Carlo Programs 1311
Appendix A All the Math You Need. . . and No More (An Executive Summary) 1317
Bibliography 1329
Index 1351
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