Derivatives Models on Models

386 Pages·2007·3.24 MB·English

by  Espen Gaarder Haug

Derivatives
Models on Models

Derivatives
Models on Models
Espen Gaarder Haug
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Contents
Author’s “Disclaimer” ix
Introduction x
Derivatives Models on Models xv
Nassim Taleb on Black Swans 1
Chapter 1 The Discovery of Fat-Tails in Price Data 17
Edward Thorp on Gambling and Trading 27
Chapter 2 Option Pricing and Hedging from Theory to Practice: Know Your
Weapon III 33
1 The Partly Ignored and Forgotten History 34
2 DiscreteDynamicDeltaHedgingunderGeometricBrownianMotion 44
3 Dynamic Delta Hedging Under Jump-Diffusion 50
4 Equilibrium Models 54
5 Portfolio Construction and Options Against Options 55
6 Conclusions 63
Alan Lewis on Stochastic Volatility and Jumps 71
Chapter 3 Back to Basics: A New Approach to the Discrete Dividend Problem 79
Together with Jørgen Haug and Alan Lewis
1 Introduction 79
2 General Solution 82
3 Dividend Models 87
4 Applications 89
Emanuel Derman the Wall Street Quant 101
Chapter 4 Closed Form Valuation of American Barrier Options 115
1 Analytical Valuation of American Barrier Options 115
vi CONTENTS
2 Numerical Comparison 116
3 Conclusion 118
Peter Carr, The Wall Street Wizard of Option Symmetry and Volatility 121
Chapter 5 Valuation of Complex Barrier Options Using Barrier Symmetry 129
1 Plain Vanilla Put–Call Symmetry 129
2 Barrier Put–Call Symmetry 130
3 Simple, Intuitive and Accurate Valuation of Double Barrier
Options 132
4 Static Hedging in the Real World 137
5 Conclusion 138
Granger on Cointegration 141
Chapter 6 Knock-in/out Margrabe 145
with Jørgen Haug
1 Margrabe Options 145
2 Knock-in/out Margrabe Options 146
3 Applications 147
Stephen Ross on APT 153
Chapter 7 Resetting Strikes, Barriers and Time 157
with Jørgen Haug
1 Introduction 157
2 Reset Strike Barrier Options 160
3 Reset Barrier Options 161
4 Resetting Time 162
5 Conclusion 163
Bruno Dupire the Stochastic Wall Street Quant 167
Chapter 8 Asian Pyramid Power 177
with Jørgen Haug and William Margrabe
1 Celia in Derivativesland 177
2 Calibrating to the Term Structure of Volatility 180
3 From Geometric to Arithmetic 184
4 The Dollars 185
Eduardo Schwartz: the Yoga Master of Mathematical Finance 191
CONTENTS vii
Chapter 9 Practical Valuation of Power Derivatives 197
1 Introduction 197
2 Energy Swaps/Forwards 199
3 Power Options 202
4 Still, What About Fat-Tails? 209
Aaron Brown on Gambling, Poker and Trading 211
Chapter 10 A Look in the Antimatter Mirror 223
1 Garbage in, Garbage Out? 223
2 Conclusion 227
Knut Aase on Catastrophes and Financial Economics 231
Chapter 11 Negative Volatility and the Survival of the Western Financial Markets 239
Knut K. Aase
1 Introduction 239
2 Negative Volatility – A Direct Approach 240
3 The Valueof a European CallOption for anyValue – Positive or Neg-
ative – of the Volatility 240
4 Negative Volatility – The Haug interpretation 242
5 Chaotic Behavior from Deterministic Dynamics 242
6 Conclusions 243
Elie Ayache on Option Trading and Modeling 247
Chapter 12 Frozen Time Arbitrage 267
1 Time Measure Arbitrage 268
2 Time Travel Arbitrage 269
3 Conclusion 273
Haug on Wilmott and Wilmott on Wilmott 277
Chapter 13 Space-time Finance The Relativity Theory’s Implications for Mathe-
matical Finance 287
1 Introduction 287
2 Time dilation 290
3 Advanced stage of Space-time Finance 292
4 Space-time Uncertainty 293
5 Is High Speed Velocity Possible? 295
6 Black-Scholes in Special Relativity 299
7 Relativity and Fat-Tailed Distributions 301
viii CONTENTS
8 General Relativity and Space-time Finance 302
9 Was Einstein Right? 305
10 Traveling Back in Time Using Wormholes 307
11 Conclusion 308
Andrei Khrennikov on Negative Probabilities 317
Chapter 14 Why so Negative about Negative Probabilities? 323
1 The History of Negative Probability 323
2 Negative Probabilities in Quantitative Finance 324
3 Getting the Negative Probabilities to Really Work in Your Favor 327
4 Hidden Variables in Finance 328
5 The Future of Negative Probabilities in Quantitative Finance 329
6 Appendix: Negative Probabilities in CRR Equivalent Trinomial Tree 330
David Bates on Crash and Jumps 335
Chapter 15 Hidden Conditions and Coin Flip Blow Up’s 343
1 Blowing Up 343
2 Coin Flip Blow Up’s 344
Peter Ja¨ckel on Monte Carlo Simulation 349
Index 359