Derivatives

Dr Espen Gaarder Haug has more than 15 years of experience in Derivatives research and trading, and has worked for more than 20 years as a trader. Until recently he worked as a proprietary trader in J.P. Morgan New York, and as a derivatives trader for two multi-billion dollar hedge funds; Amaranth Investor and Paloma Partners, located in Greenwich Connecticut. Before that he worked for Tempus Financial Engineering, Chase Manhattan Bank (now J.P. Morgan Chase) and Den Norske Bank. He is the author of The Complete Guide of Option Pricing Formulas, which has become a reference manual among Wall Street professionals. He has a PhD from the Norwegian University of Science and Technology where he specialized in Option Valuation and Trading and has published extensively in practitioner and academic journals. He is currently considering setting up his own investment company - possibly the first Anti-Hedge fund!

• Author’s “Disclaimer” ixIntroduction xDerivatives Models on Models xvNassim Taleb on Black Swans 1Chapter 1 The Discovery of Fat-Tails in Price Data 17Edward Thorp on Gambling and Trading 27Chapter 2 Option Pricing and Hedging from Theory to Practice: Know Your Weapon III 331 The Partly Ignored and Forgotten History 342 Discrete Dynamic Delta Hedging under Geometric Brownian Motion 443 Dynamic Delta Hedging Under Jump-Diffusion 504 Equilibrium Models 545 Portfolio Construction and Options Against Options 556 Conclusions 63Alan Lewis on Stochastic Volatility and Jumps 71Chapter 3 Back to Basics: A New Approach to the Discrete Dividend Problem 79Together with Jørgen Haug and Alan Lewis1 Introduction 792 General Solution 823 Dividend Models 874 Applications 89Emanuel Derman the Wall Street Quant 101Chapter 4 Closed Form Valuation of American Barrier Options 1151 Analytical Valuation of American Barrier Options 1152 Numerical Comparison 1163 Conclusion 118Peter Carr, The Wall Street Wizard of Option Symmetry and Volatility 121Chapter 5 Valuation of Complex Barrier Options Using Barrier Symmetry 1291 Plain Vanilla Put–Call Symmetry 1292 Barrier Put–Call Symmetry 1303 Simple, Intuitive and Accurate Valuation of Double Barrier Options 1324 Static Hedging in the Real World 1375 Conclusion 138Granger on Cointegration 141Chapter 6 Knock-in/out Margrabe 145with Jørgen Haug1 Margrabe Options 1452 Knock-in/out Margrabe Options 1463 Applications 147Stephen Ross on APT 153Chapter 7 Resetting Strikes, Barriers and Time 157with Jørgen Haug1 Introduction 1572 Reset Strike Barrier Options 1603 Reset Barrier Options 1614 Resetting Time 1625 Conclusion 163Bruno Dupire the Stochastic Wall Street Quant 167Chapter 8 Asian Pyramid Power 177with Jørgen Haug and William Margrabe1 Celia in Derivativesland 1772 Calibrating to the Term Structure of Volatility 1803 From Geometric to Arithmetic 1844 The Dollars 185Eduardo Schwartz: the Yoga Master of Mathematical Finance 191Chapter 9 Practical Valuation of Power Derivatives 1971 Introduction 1972 Energy Swaps/Forwards 1993 Power Options 2024 Still, What About Fat-Tails? 209Aaron Brown on Gambling, Poker and Trading 211Chapter 10 A Look in the Antimatter Mirror 2231 Garbage in, Garbage Out? 2232 Conclusion 227Knut Aase on Catastrophes and Financial Economics 231Chapter 11 Negative Volatility and the Survival of the Western Financial Markets 239Knut K. Aase1 Introduction 2392 Negative Volatility – A Direct Approach 2403 The Value of a European Call Option for any Value – Positive or Negative – of the Volatility 2404 Negative Volatility – The Haug interpretation 2425 Chaotic Behavior from Deterministic Dynamics 2426 Conclusions 243Elie Ayache on Option Trading and Modeling 247Chapter 12 Frozen Time Arbitrage 2671 Time Measure Arbitrage 2682 Time Travel Arbitrage 2693 Conclusion 273Haug on Wilmott and Wilmott on Wilmott 277Chapter 13 Space-time Finance The Relativity Theory’s Implications for Mathematical Finance 2871 Introduction 2872 Time dilation 2903 Advanced stage of Space-time Finance 2924 Space-time Uncertainty 2935 Is High Speed Velocity Possible? 2956 Black-Scholes in Special Relativity 2997 Relativity and Fat-Tailed Distributions 3018 General Relativity and Space-time Finance 3029 Was Einstein Right? 30510 Traveling Back in Time Using Wormholes 30711 Conclusion 308Andrei Khrennikov on Negative Probabilities 317Chapter 14 Why so Negative about Negative Probabilities? 3231 The History of Negative Probability 3232 Negative Probabilities in Quantitative Finance 3243 Getting the Negative Probabilities to Really Work in Your Favor 3274 Hidden Variables in Finance 3285 The Future of Negative Probabilities in Quantitative Finance 3296 Appendix: Negative Probabilities in CRR Equivalent Trinomial Tree 330David Bates on Crash and Jumps 335Chapter 15 Hidden Conditions and Coin Flip Blow Up’s 3431 Blowing Up 3432 Coin Flip Blow Up’s 344Peter Jáckel on Monte Carlo Simulation 349Index 359