The Heston model and its extensions in Matlab and C#
Tap into the power of the most popular stochastic volatility model for pricing equity derivatives Since its introduction in 1993, the Heston model has become a popular model for pricing equity derivatives, and the most popular stochastic volatility model in financial engineering. This vital resource...
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| Main Authors: | , |
|---|---|
| Format: | eBook Book |
| Language: | English |
| Published: |
Hoboken, N. J
John Wiley & Sons
2013
Wiley John Wiley & Sons, Incorporated Wiley-Blackwell |
| Edition: | 1 |
| Series: | Wiley finance series |
| Subjects: | |
| ISBN: | 9781118548257, 1118548256, 9781118695173, 1118695178 |
| Online Access: | Get full text |
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Table of Contents:
- Pathwise Adapted Linearization Quadratic -- Kahl-Ja¨ ckel IJK Scheme -- Quadratic-Exponential Scheme -- Moment-Matching -- Process for the Log-Stock Price -- Martingale Correction -- Alfonsi Scheme for the Variance -- Moment Matching Scheme -- Conclusion -- Chapter 8 American Options -- Least-Squares Monte Carlo -- The Explicit Method -- Beliaeva-Nawalkha Bivariate Tree -- Trinomial Tree for the Variance -- Trinomial Tree for the Stock Price -- Combining the Trinomial Trees -- Computer Implementation -- Medvedev-Scaillet Expansion -- Medvedev-Scaillet for Black-Scholes -- Medvedev-Scaillet for Heston -- Parameter Estimation -- Chiarella and Ziogas American Call -- Early Exercise Boundary Approximation -- The American Call Price -- Estimating the Early Exercise Boundary -- 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 No¨gel Model -- Parameter Estimation -- Elices Model -- Benhamou-Miri-Gobet Model -- Constant Parameters -- Piecewise Constant Parameters -- Parameter Estimation -- Black-Scholes Derivatives -- Conclusion -- Chapter 10 Methods for Finite Differences -- The PDE in Terms of an Operator -- Building Grids -- Finite Difference Approximation of Derivatives -- The Weighted Method -- Boundary Conditions for the PDE -- Explicit Scheme -- Error Analysis -- ADI Schemes -- Conclusion -- Chapter 11 The Heston Greeks -- Analytic Expressions for European Greeks -- Delta, Gamma, Rho, Theta, and Vega -- Vanna, Volga, and Other 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
- Cover -- Title Page -- Copyright -- Contents -- Foreword -- Preface -- Acknowledgments -- Chapter 1 The Heston Model for European Options -- Model Dynamics -- Properties of the Variance Process -- The European Call Price -- The Heston PDE -- Setting Up the Hedging Portfolio -- The PDE for the Option Price -- The PDE for P1 and P2 -- Obtaining the Heston Characteristic Functions -- Solving the Heston Riccati Equation -- The Riccati Equation in a General Setting -- Solution of the Heston Riccati Equation -- Dividend Yield and the Put Price -- Consolidating the Integrals -- Black-Scholes as a Special Case -- Summary of the Call Price -- 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 -- Heston Terminal Spot Price -- Effect of Correlation and Volatility of Variance -- Comparison With Black-Scholes Prices -- Heston Implied Volatility -- Variance Modeling in the Heston Model -- Variance Swap -- Dupire Local Volatility -- Local Volatility With Finite Differences -- Approximate Local Volatility -- Numerical Illustration of Local Volatility -- Implied Volatility -- Moment Explosions -- Bounds on Implied Volatility Slope -- Conclusion -- Chapter 3 Derivations Using the Fourier Transform -- The Fourier Transform -- Recovery of Probabilities With Gil-Pelaez Fourier Inversion -- Derivation of Gatheral (2006) -- Attari (2004) Representation -- Carr and Madan (1999) Representation -- Bounds on the Carr-Madan Damping Factor and Optimal Value -- Optimal Damping Factor -- Numerical Implementation and Illustration -- The Carr-Madan Representation for Puts -- The Representation for OTM Options -- Generalization of the OTM Representation -- Conclusion
- Chapter 4 The Fundamental Transform for Pricing Options -- The Payoff Transform -- The Fundamental Transform and the Option Price -- The Fundamental Transform for the Heston Model -- The Call Price Using the Fundamental Transform -- Option Prices Using Parseval's Identity -- Parseval's Identity -- The Option Price Using Parseval's Identity -- Parseval's Identity for the Heston Model -- Contour Variations and the Call Price -- Volatility of Volatility Series Expansion -- Conclusion -- Chapter 5 Numerical Integration Schemes -- The Integrand in Numerical Integration -- Newton-Cotes Formulas -- Mid-point Rule -- Trapezoidal Rule -- Trapezoidal Rule for Double Integrals -- Simpson's Rule -- Simpson's Three-Eighths Rule -- Gaussian Quadrature -- Gauss-Laguerre Quadrature -- Gauss-Legendre Quadrature -- Gauss-Lobatto Quadrature -- Gaussian Quadrature for Double Integrals -- Gaussian Quadrature in C# -- Integration Limits and Kahl and J¨ackel Transformation -- Illustration of Numerical Integration -- Fast Fourier Transform -- Discretization of the Integration Range and of the Strike Range -- Summary of the FFT -- Fractional Fast Fourier Transform -- Conclusion -- Chapter 6 Parameter Estimation -- Estimation Using Loss Functions -- Nelder-Mead Algorithm in C# -- Starting Values -- 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 -- Euler Scheme for the Variance -- Euler Scheme for the Stock Price -- Milstein Scheme -- Milstein Scheme for the Heston Model -- Milstein Scheme for the Variance -- Milstein Scheme for the Stock Price -- Implicit Milstein Scheme -- Transformed Volatility Scheme -- Balanced, Pathwise, and IJK Schemes -- Balanced Implicit Scheme
- 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 -- Simulation of the Stock Price -- Euler Scheme for the Variance -- Alfonsi Scheme for the Variance -- Zhu Scheme for the Transformed Variance -- Quadratic Exponential Scheme -- American Options in the Double Heston Model -- Conclusion -- Bibliography -- About the Website -- Index