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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| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
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Hoboken, N. J
John Wiley & Sons
2013
Wiley John Wiley & Sons, Incorporated Wiley-Blackwell |
| Vydání: | 1 |
| Edice: | Wiley finance series |
| Témata: | |
| ISBN: | 9781118548257, 1118548256, 9781118695173, 1118695178 |
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| Abstract | 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 provides a thorough derivation of the original model, and includes the most important extensions and refinements that have allowed the model to produce option prices that are more accurate and volatility surfaces that better reflect market conditions. The book's material is drawn from research papers and many of the models covered and the computer codes are unavailable from other sources.
The book is light on theory and instead highlights the implementation of the models. All of the models found here have been coded in Matlab and C#. This reliable resource offers an understanding of how the original model was derived from Ricatti equations, and shows how to implement implied and local volatility, Fourier methods applied to the model, numerical integration schemes, parameter estimation, simulation schemes, American options, the Heston model with time-dependent parameters, finite difference methods for the Heston PDE, the Greeks, and the double Heston model.
* A groundbreaking book dedicated to the exploration of the Heston model—a popular model for pricing equity derivatives
* Includes a companion website, which explores the Heston model and its extensions all coded in Matlab and C#
* Written by Fabrice Douglas Rouah a quantitative analyst who specializes in financial modeling for derivatives for pricing and risk management
Engaging and informative, this is the first book to deal exclusively with the Heston Model and includes code in Matlab and C# for pricing under the model, as well as code for parameter estimation, simulation, finite difference methods, American options, and more. |
|---|---|
| AbstractList | 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 provides a thorough derivation of the original model, and includes the most important extensions and refinements that have allowed the model to produce option prices that are more accurate and volatility surfaces that better reflect market conditions. The book's material is drawn from research papers and many of the models covered and the computer codes are unavailable from other sources.
The book is light on theory and instead highlights the implementation of the models. All of the models found here have been coded in Matlab and C#. This reliable resource offers an understanding of how the original model was derived from Ricatti equations, and shows how to implement implied and local volatility, Fourier methods applied to the model, numerical integration schemes, parameter estimation, simulation schemes, American options, the Heston model with time-dependent parameters, finite difference methods for the Heston PDE, the Greeks, and the double Heston model.
* A groundbreaking book dedicated to the exploration of the Heston model—a popular model for pricing equity derivatives
* Includes a companion website, which explores the Heston model and its extensions all coded in Matlab and C#
* Written by Fabrice Douglas Rouah a quantitative analyst who specializes in financial modeling for derivatives for pricing and risk management
Engaging and informative, this is the first book to deal exclusively with the Heston Model and includes code in Matlab and C# for pricing under the model, as well as code for parameter estimation, simulation, finite difference methods, American options, and more. 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 provides a thorough derivation of the original model, and includes the most important extensions and refinements that have allowed the model to produce option prices that are more accurate and volatility surfaces that better reflect market conditions. The book's material is drawn from research papers and many of the models covered and the computer codes are unavailable from other sources. The book is light on theory and instead highlights the implementation of the models. All of the models found here have been coded in Matlab and C#. This reliable resource offers an understanding of how the original model was derived from Ricatti equations, and shows how to implement implied and local volatility, Fourier methods applied to the model, numerical integration schemes, parameter estimation, simulation schemes, American options, the Heston model with time-dependent parameters, finite difference methods for the Heston PDE, the Greeks, and the double Heston model. A groundbreaking book dedicated to the exploration of the Heston model-a popular model for pricing equity derivatives Includes a companion website, which explores the Heston model and its extensions all coded in Matlab and C# Written by Fabrice Douglas Rouah a quantitative analyst who specializes in financial modeling for derivatives for pricing and risk management Engaging and informative, this is the first book to deal exclusively with the Heston Model and includes code in Matlab and C# for pricing under the model, as well as code for parameter estimation, simulation, finite difference methods, American options, and more. |
| Author | Heston, Steven L. Rouah, Fabrice |
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| Notes | "+website"--Cover Includes index Bibliography: p. 383-389 |
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| Snippet | 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... 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... |
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| SubjectTerms | C# (Computer program language) Dynamische Wirtschaftstheorie Finance Finance -- Mathematical models Mathamatical models Mathematical models MATLAB MATLAB (Computer program) Options (Finance) Options (Finance) -- Mathematical models Options (Finance) -- Prices Optionspreistheorie Prices Prizes Programmiersprache |
| TableOfContents | 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 |
| Title | The Heston model and its extensions in Matlab and C# |
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