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CONTENTS
Preface ... xi
1 The quantitative finance timeline / Paul Wilmott ... 1
1827 Brown ... 1
1900 Bachelier ... 1
1905 Einstein ... 1
1923 Wiener ... 1
1950s Samuelson ... 1
19...
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CONTENTS
Preface ... xi
1 The quantitative finance timeline / Paul Wilmott ... 1
1827 Brown ... 1
1900 Bachelier ... 1
1905 Einstein ... 1
1923 Wiener ... 1
1950s Samuelson ... 1
1951 It<?import namespace ... m ur
1952 Markowitz ... 2
1963 Sharpe, Lintner and Mossin ... 3
1966 Fama ... 3
1960s Sobol', Faure, Hammersley, Haselgrove, Halton... ... 3
1968 Thorp ... 4
1973 Black, Scholes and Merton ... 4
1977 Boyle ... 5
1977 Vasicek ... 5
1979 Cox, Ross, Rubinstein ... 6
1979-81 Harrison, Kreps, Pliska ... 6
1986 Ho and Lee ... 7
1992 Heath, Jarrow and Morton ... 7
1990s Credit risk ... 7
1990s Cheyette, Barrett, Moore, Wilmoltt ... 7
1994 Dupire, Rubinstein, Derman and Kani ... 8
1996 Avellaneda and Par<m:math xmlns ... '"htt
And the Nobel Prize for Economics goes to... ... 9
Bibliography ... 9
Part One New Directions in Equity Modelling ... 11
2 Introduction ... 13
Chapters 3 to 6 ... 14
Asymptotic analysis of stochastic volatility models ... 14
Passport options : a review ... 15
Equity dividend models ... 15
Isoperimetry, log-concavity and elasticity of option prices ... 16
Models needed ... 16
Bibliography ... 17
3 Asymptotic analysis of stochastic volatility models / Henrik Rasmussen ; Paul Wilmott ... 19
Introduction ... 19
Conditions on the models ... 20
Examples of models ... 21
Scott's model ... 21
The Heston/Ball-Roma model ... 22
Notation ... 22
Asymptotic analysis ... 23
Vanilla options : asymptotics for values ... 26
Vanilla options : implied volatilities ... 28
Acknowledgement ... 31
References ... 31
4 Passport options : a review / Antony Penaud ... 33
Introduction ... 33
The vanilla passport option ... 34
The stochastic control approach ... 34
The martingale approach ... 36
Utility of trading passport ... 37
Exotic passport options ... 42
Multi-asset passport option ... 42
Discrete trading constraints ... 44
Vacation calls and vacation puts ... 47
Miscellaneous exotic ... 49
Conclusion ... 51
References ... 52
5 Equity dividend models / David Bakstein ; Paul Wilmott ... 55
Introduction ... 55
Effects of dividends on asset prices ... 56
Frictionless markets ... 56
Market frictions ... 57
Non-stochastic dividend models ... 58
Known dividends ... 58
Non-Markovian models ... 61
Non-linear models ... 62
Stochastic dividend models ... 66
Diffusive dividend processes ... 66
Random jump processes ... 68
Criteria for model choice and summary ... 69
Sensitivity ratios ... 70
Time to expiry ... 70
Computational cost ... 70
Type of instrument ... 70
References ... 71
6 Isoperimetry, log-concavity and elasticity of option prices / Christer Borell ... 73
Introduction ... 73
A brief review of isoperimetry in option pricing ... 73
Log-concavity ... 76
Log-concavity applied to option pricing ... 84
References ... 91
Part Two New Directions in Interest Rate Modelling ... 93
7 Introduction ... 95
Chapters 8 and 9 ... 96
Dynamic, deterministic and static optimal portfolio strategies in a mean-variance framework under stochastic interest rates ... 96
Pricing bond options in a worst-case scenario ... 97
Models needed ... 98
Bibliography ... 99
8 Dynamic, deterministic and static optimal portfolio strategies in a mean-variance framework under stochastic interest rates / Isabelle Bajeux-Besnainou ; Roland Portait ... 101
Introduction ... 101
The framework ... 102
Mean-variance efficient strategies when stochastic rebalancing is allowed ... 104
Predetermined weights : deterministic mean-variance dynamic efficiency ... 105
Buy-and-hold strategies ... 106
Simulations and comparison of the different cases ... 107
Appendix A ... 108
Appendix B ... 113
Notes ... 114
References ... 114
9 Pricing bond options in a worst-case scenario / David Epstein ; Paul Wilmott ... 117
Introduction ... 117
A worst-case scenario valuation ... 118
The pricing problem with optionality ... 119
Pricing a European option on a zero-coupon bond ... 119
Hedging the European option with the underlying zero-coupon bond ... 121
Hedging the European option with other instruments ... 123
Pricing and hedging American options ... 128
Conclusion ... 131
References ... 132
Part Three New Directions in Risk Management ... 135
10 Introduction ... 137
Chapters 11 to 13 ... 137
Implementing VaR by historical simulation ... 137
CrashMetrics ... 138
Herding in financial markets : a role for psychology in explaining investor behaviour? ... 138
Models needed ... 138
Bibliography ... 139
11 Implementing VaR by historical simulation / Aldo Nassigh ; Andrea Piazzetta ; Ferdinando Sama ... 141
Introduction ... 141
Historical simulation : the partial revaluation approach ... 141
Implementing Value at Risk : a practical example ... 144
Conclusion ... 151
References ... 151
12 CrashMetrics / Philip Hua ; Paul Wilmott ... 153
Introduction ... 153
Why do banks go broke? ... 153
Market crashes ... 153
CrashMetrics ... 154
CrashMetrics for one stock ... 155
Portfolio optimisation and the Platinum Hedge ... 157
The multi-asset/single-index model ... 157
Portfolio optimisation and the Platinum Hedge in the multi-asset model ... 161
The multi-index model ... 162
Crash dispersion ... 163
Bias effects ... 163
Analysis of data ... 164
Margin calls and margin hedging ... 165
What is margin? ... 165
Modelling margin ... 165
Counterparty risk ... 166
Simple extensions to CrashMetrics ... 166
The CrashMetrics Index ... 166
Summary ... 167
Further reading ... 167
13 Herding in financial markets : a role for psychology in explaining investor behaviour? / Henri<m:math xmlns ... '"htt
Introduction ... 169
Herding in economic theory ... 169
Psychology in finance : existing research ... 172
The psychology of crowd behaviour : the theory of cognitive dissonance ... 174
Principle of congruity ... 174
The theory of cognitive dissonance ... 174
Conclusions ... 177
Notes ... 178
References ... 179
Further reading ... 181
Author biographies ... 183
Index ... 187
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