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The Heston Model and its Extensions in Matlab and C Website 1st Edition by Fabrice D Rouah, Steven L Heston ISBN 1118548256 9781118548257

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The Heston Model and its Extensions in Matlab and C Website 1st Edition Fabrice D. Rouah Digital Instant Download

Author(s): Fabrice D. Rouah, Steven L. Heston
ISBN(s): 9781118548257, 1118548256
Edition: 1
File Details: PDF, 4.70 MB
Year: 2013
Language: english
SKU: EB-4682438 Category: Tags: ,

The Heston Model and its Extensions in Matlab and C Website 1st Edition by Fabrice D Rouah, Steven L Heston – Ebook PDF Instant Download/Delivery: 1118548256, 9781118548257
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ISBN 10: 1118548256 
ISBN 13: 9781118548257
Author: Fabrice D Rouah, Steven L Heston

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.

The Heston Model and its Extensions in Matlab and C Website 1st Table of contents:

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 Jäckel 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
Pathwise Adapted Linearization Quadratic
Kahl-Jäckel 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 Nögel 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
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

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