The Heston model and its extensions in VBA - Rouah, Fabrice, 1964- (Wiley, 2015)
Machine generated contents note: Foreword Preface Acknowledgments About This Book VBA Library for Complex Numbers Chapter 1: The Heston Model for European Options Model Dynamics The Heston European Call Price Dividend Yield and the Put Price Consolidating the Integrals Black-Scholes as a Special Case Conclusion Chapter 2: Integration Issues, Parameter Effects, and Variance Modeling Remarks on the Characteristic Functions Problems With the Integrand The Little Heston Trap Effect of the Heston Parameters Variance Modeling in the Heston Model Moment Explosions Bounds on Implied Volatility Slope Conclusion Chapter 3: Derivations Using the Fourier Transform Derivation of Gatheral (2006) Attari (2004) Representation Carr and Madan (1999) Representation Conclusion Chapter 4: The Fundamental Transform for Pricing Options The Payoff Transform Option Prices Using Parseval's Identity Volatility of Volatility Series Expansion Conclusion Chapter 5: Numerical Integration Schemes The Integrand in Numerical Integration Newton-Cotes Formulas Gaussian Quadrature Integration Limits, Multi-Domain Integration, and Kahl and Jackel Transformation Illustration of Numerical Integration Fast Fourier Transform Fractional Fast Fourier Transform Conclusion Chapter 6: Parameter Estimation Estimation Using Loss Functions Speeding up the Estimation Differential Evolution Maximum Likelihood Estimation Risk-Neutral Density and Arbitrage-Free Volatility Surface Conclusion Chapter 7: Simulation in the Heston Model General Setup Euler Scheme Milstein Scheme Implicit Milstein Scheme Transformed Volatility Scheme Balanced, Pathwise, and IJK Schemes Quadratic-Exponential Scheme Alfonsi Scheme for the Variance Moment Matching Scheme Conclusion Chapter 8: American Options Least-Squares Monte Carlo The Explicit Method Beliaeva-Nawalkha Bivariate Tree Medvedev-Scaillet Expansion Chiarella and Ziogas American Call Conclusion Chapter 9: Time-Dependent Heston Models Generalization of the Riccati Equation Bivariate Characteristic Function Linking the Bivariate CF and the General Riccati Equation Mikhailov and Nogel Model Elices Model Benhamou-Miri-Gobet Model Black-Scholes Derivatives Conclusion Chapter 10: Methods for Finite Differences The PDE in Terms of an Operator Building Grids Finite Difference Approximation of Derivatives Boundary Conditions for the PDE The Weighted Method Explicit Scheme ADI Schemes Conclusion Chapter 11: The Heston Greeks Analytic Expressions for European Greeks Finite Differences for the Greeks Numerical Implementation of the Greeks Greeks Under the Attari and Carr-Madan Formulations Greeks Under the Lewis Formulations Greeks Using the FFT and FRFT American Greeks Using Simulation American Greeks Using the Explicit Method American Greeks from Medvedev and Scaillet Conclusion Chapter 12: The Double Heston Model Multi-Dimensional Feynman-Kac Theorem Double Heston Call Price Double Heston Greeks Parameter Estimation Simulation in the Double Heston Model American Options in the Double Heston Model Conclusion Bibliography About the Website Index .