The Heston Model and Its Extensions in Matlab and C#

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av Fabrice Douglas Rouah  (häftad, 2013)

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The Heston Model and Its Extensions in Matlab and C# (häftad)

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  • Häftad (paperback)
  • Språk: Engelska
  • Antal sidor: 432
  • Utg.datum: 2013-10-18
  • Upplaga: 1
  • Förlag: John Wiley & Sons Inc
  • Medarbetare: Heston, Steven L. (foreword)
  • Illustrationer: illustrations
  • Dimensioner: 254 x 177 x 25 mm
  • Vikt: 743 g
  • Antal komponenter: 1
  • ISBN: 9781118548257

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Bloggat om The Heston Model and Its Extensions in Matlab and C#

Övrig information

<p>FABRICE DOUGLAS ROUAH is a quantitative analyst who specializes in financial modeling of derivatives for pricing and risk management at Sapient Global Markets, a global consultancy. Prior to joining Sapient, Rouah worked at State Street Corporation and McGill University. He is the coauthor and/or coeditor of five books on hedge funds, commodity trading advisors, and option pricing. Rouah holds a PhD in finance and an MSc in statistics from McGill University, and a BSc in applied mathematics from Concordia University.


<p>Foreword ix <p>Preface xi <p>Acknowledgments xiii <p>CHAPTER 1 The Heston Model for European Options 1 <p>Model Dynamics 1 <p>The European Call Price 4 <p>The Heston PDE 5 <p>Obtaining the Heston Characteristic Functions 10 <p>Solving the Heston Riccati Equation 12 <p>Dividend Yield and the Put Price 17 <p>Consolidating the Integrals 18 <p>Black-Scholes as a Special Case 19 <p>Summary of the Call Price 22 <p>Conclusion 23 <p>CHAPTER 2 Integration Issues, Parameter Effects, and Variance Modeling 25 <p>Remarks on the Characteristic Functions 25 <p>Problems With the Integrand 29 <p>The Little Heston Trap 31 <p>Effect of the Heston Parameters 34 <p>Variance Modeling in the Heston Model 43 <p>Moment Explosions 56 <p>Bounds on Implied Volatility Slope 57 <p>Conclusion 61 <p>CHAPTER 3 Derivations Using the Fourier Transform 63 <p>The Fourier Transform 63 <p>Recovery of Probabilities With Gil-Pelaez Fourier Inversion 65 <p>Derivation of Gatheral (2006) 67 <p>Attari (2004) Representation 69 <p>Carr and Madan (1999) Representation 73 <p>Bounds on the Carr-Madan Damping Factor and Optimal Value 76 <p>The Carr-Madan Representation for Puts 82 <p>The Representation for OTM Options 84 <p>Conclusion 89 <p>CHAPTER 4 The Fundamental Transform for Pricing Options 91 <p>The Payoff Transform 91 <p>The Fundamental Transform and the Option Price 92 <p>The Fundamental Transform for the Heston Model 95 <p>Option Prices Using Parseval s Identity 100 <p>Volatility of Volatility Series Expansion 108 <p>Conclusion 113 <p>CHAPTER 5 Numerical Integration Schemes 115 <p>The Integrand in Numerical Integration 116 <p>Newton-Cotes Formulas 116 <p>Gaussian Quadrature 121 <p>Integration Limits and Kahl and J ¨ ackel Transformation 130 <p>Illustration of Numerical Integration 136 <p>Fast Fourier Transform 137 <p>Fractional Fast Fourier Transform 141 <p>Conclusion 145 <p>CHAPTER 6 Parameter Estimation 147 <p>Estimation Using Loss Functions 147 <p>Speeding up the Estimation 158 <p>Differential Evolution 162 <p>Maximum Likelihood Estimation 166 <p>Risk-Neutral Density and Arbitrage-Free Volatility Surface 170 <p>Conclusion 175 <p>CHAPTER 7 Simulation in the Heston Model 177 <p>General Setup 177 <p>Euler Scheme 179 <p>Milstein Scheme 181 <p>Milstein Scheme for the Heston Model 183 <p>Implicit Milstein Scheme 185 <p>Transformed Volatility Scheme 188 <p>Balanced, Pathwise, and IJK Schemes 191 <p>Quadratic-Exponential Scheme 193 <p>Alfonsi Scheme for the Variance 198 <p>Moment Matching Scheme 201 <p>Conclusion 202 <p>CHAPTER 8 American Options 205 <p>Least-Squares Monte Carlo 205 <p>The Explicit Method 213 <p>Beliaeva-Nawalkha Bivariate Tree 217 <p>Medvedev-Scaillet Expansion 228 <p>Chiarella and Ziogas American Call 253 <p>Conclusion 261 <p>CHAPTER 9 Time-Dependent Heston Models 263 <p>Generalization of the Riccati Equation 263 <p>Bivariate Characteristic Function 264 <p>Linking the Bivariate CF and the General Riccati Equation 269 <p>Mikhailov and No¨ gel Model 271 <p>Elices Model 278 <p>Benhamou-Miri-Gobet Model 285 <p>Black-Scholes Derivatives 299 <p>Conclusion 300 <p>CHAPTER 10 Methods for Finite Differences 301 <p>The PDE in Terms of an Operator 301 <p>Building Grids 302 <p>Finite Difference Approximation of Derivatives 303 <p>The Weighted Method 306 <p>Boundary Conditions for the PDE 315 <p>Explicit Scheme 316 <p>ADI

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