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Derivatives Models on Models

Book Description

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

"The ebook version does not provide access to the companion files".

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Contents
  5. Author's “Disclaimer”
  6. Introduction
  7. Derivatives Models on Models
  8. Nassim Taleb on Black Swans
  9. 1: The Discovery of Fat-Tails in Price Data
  10. Edward Thorp on Gambling and Trading
  11. 2: Option Pricing and Hedging from Theory to Practice: Know Your Weapon III *
    1. 1 The Partly Ignored and Forgotten History
    2. 2 Discrete Dynamic Delta Hedging Under Geometric Brownian Motion
    3. 3 Dynamic Delta Hedging Under Jump-diffusion
    4. 4 Equilibrium Models
    5. 5 Portfolio Construction and Options Against Options
    6. 6 Conclusions
  12. Alan Lewis on Stochastic Volatility and Jumps
  13. 3: Back to Basics: A New Approach to the Discrete Dividend Problem *
    1. 1 Introduction
    2. 2 General Solution
    3. 3 Dividend Models
    4. 4 Applications
    5. Appendix A
    6. Appendix B
  14. Emanuel Derman the Wall Street Quant
  15. 4: Closed Form Valuation of American Barrier Options *
    1. 1 Analytical Valuation of American Barrier Options
    2. 2 Numerical Comparison
    3. 3 Conclusion
  16. Peter Carr, The Wall Street Wizard of Option Symmetry and Volatility
  17. 5: Valuation of Complex Barrier Options Using Barrier Symmetry *
    1. 1 Plain Vanilla Put–Call Symmetry
    2. 2 Barrier Put–Call Symmetry
    3. 3 Simple, Intuitive and Accurate Valuation of Double Barrier Options
    4. 4 Static Hedging in the Real World
    5. 5 Conclusion
  18. Granger on Cointegration
  19. 6: Knock-in/Out Margrabe *
    1. 1 Margrabe Options
    2. 2 Knock-in/out Margrabe Options
    3. 3 Applications
    4. Appendix
  20. Stephen Ross on APT
  21. 7: Resetting Strikes, Barriers and Time *
    1. 1 Introduction
    2. 2 Reset Strike Barrier Options
    3. 3 Reset Barrier Options
    4. 4 Resetting Time
    5. 5 Conclusion
  22. Bruno Dupire the Stochastic Wall Street Quant
  23. 8: Asian Pyramid Power
    1. 1 Celia in Derivativesland
    2. 2 Calibrating to the Term Structure of Volatility
    3. 3 From Geometric to Arithmetic
    4. 4 The Dollars
    5. Appendix: Inside the Average Period
  24. Eduardo Schwartz: The Yoga Master of Mathematical Finance
  25. 9: Practical Valuation of Power Derivatives *
    1. 1 Introduction
    2. 2 Energy Swaps/Forwards
    3. 3 Power Options
    4. 4 Still, What About Fat-Tails?
  26. Aaron Brown on Gambling, Poker and Trading
  27. 10: A Look in the Antimatter Mirror *
    1. 1 Garbage in, Garbage Out?
    2. 2 Conclusion
  28. Knut Aase on Catastrophes and Financial Economics
  29. 11: Negative Volatility and the Survival of the Western Financial Markets
    1. 1 Introduction
    2. 2 Negative Volatility – A Direct Approach
    3. 3 The Value of a European Call Option for any Value – Positive or Negative – of the Volatility
    4. 4 Negative Volatility – The Haug Interpretation
    5. 5 Chaotic Behavior from Deterministic Dynamics
    6. 6 Conclusions
  30. Elie Ayache on Option Trading and Modeling
  31. 12: Frozen Time Arbitrage *
    1. 1 Time Measure Arbitrage
    2. 2 Time Travel Arbitrage
    3. 3 Conclusion
  32. Haug on Wilmott and Wilmott on Wilmott
  33. 13: Space-time Finance the Relativity Theory's Implications for Mathematical Finance *
    1. 1 Introduction
    2. 2 Time Dilation
    3. 3 Advanced Stage of Space-time Finance
    4. 4 Space-time Uncertainty
    5. 5 Is High Speed Velocity Possible?
    6. 6 Black-scholes in Special Relativity
    7. 7 Relativity and Fat-Tailed Distributions
    8. 8 General Relativity and Space-time Finance
    9. 9 Was Einstein Right?
    10. 10 Traveling Back in Time Using Wormholes
    11. 11 Conclusion
    12. Appendix A: Special Relativity and Time Dilation
    13. Appendix B: Relationship between Acceleration in Different Frames
  34. Andrei Khrennikov on Negative Probabilities
  35. 14: Why So Negative About Negative Probabilities? *
    1. 1 The History of Negative Probability
    2. 2 Negative Probabilities in Quantitative Finance
    3. 3 Getting the Negative Probabilities to Really Work in Your Favor
    4. 4 Hidden Variables in Finance
    5. 5 The Future of Negative Probabilities in Quantitative Finance
    6. 6 Appendix: Negative Probabilities in CRR Equivalent Trinomial Tree
  36. David Bates on Crash and Jumps
  37. 15: Hidden Conditions and Coin Flip Blow Up's *
    1. 1 Blowing Up
    2. 2 Coin Flip Blow Up's
  38. Peter Jäckel on Monte Carlo Simulation
  39. Index