Derivatives: Models on Models

Derivatives Models on Models takes a theoretical and practical look at some of the latest and most important ideas behind derivatives pricing models. In each chapter the author highlights the latest thinking and trends in the area. A wide range of topics are covered, including valuation methods on stocks paying discrete dividend, Asian options, American barrier options, Complex barrier options, reset options, and electricity derivatives. The book also discusses the latest ideas surrounding finance like the robustness of dynamic delta hedging, option hedging, negative probabilities and space-time finance. The accompanying CD-ROM with additional Excel sheets includes the mathematical models covered in the book. The book also includes interviews with some of the world’s top names in the industry, and an insight into the history behind some of the greatest discoveries in quantitative finance. Interviewees include: Clive Granger, Nobel Prize winner in Economics 2003, on Cointegration Nassim Taleb on Black Swans Stephen Ross on Arbitrage Pricing Theory Emanuel Derman the Wall Street Quant Edward Thorp on Gambling and Trading Peter Carr the Wall Street Wizard of Option Symmetry and Volatility Aaron Brown on Gambling, Poker and Trading David Bates on Crash and Jumps Andrei Khrennikov on Negative Probabilities Elie Ayache on Option Trading and Modeling Peter Jaeckel on Monte Carlo Simulation Alan Lewis on Stochastic Volatility and Jumps Paul Wilmott on Paul Wilmott Knut Aase on Catastrophes and Financial Economics Eduardo Schwartz the Yoga Master of Quantitative Finance Bruno Dupire on Local and Stochastic Volatility Models

Table of 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 Discrete Dynamic Delta Hedging under Geometric Brownian Motion 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 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 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 Value of a European Call Option for any Value – Positive or Negative – 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 Mathematical 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 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 Jáckel on Monte Carlo Simulation 349 Index 359