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The Heston Model and Its Extensions in VBA


Practical options pricing for better-informed investment decisions.

The Heston Model and Its Extensions in VBA is the definitive guide to options pricing using two of the derivatives industry's most powerful modeling tools—the Heston model, and VBA. Light on theory, this extremely useful reference focuses on implementation, and can help investors more efficiently—and accurately—exploit market information to better inform investment decisions. Coverage includes a description of the Heston model, with specific emphasis on equity options pricing and variance modeling, The book focuses not only on the original Heston model, but also on the many enhancements and refinements that have been applied to the model, including methods that use the Fourier transform, numerical integration schemes, simulation, methods for pricing American options, and much more. The companion website offers pricing code in VBA that resides in an extensive set of Excel spreadsheets.

The Heston model is the derivatives industry's most popular stochastic volatility model for pricing equity derivatives. This book provides complete guidance toward the successful implementation of this valuable model using the industry's ubiquitous financial modeling software, giving users the understanding—and VBA code—they need to produce option prices that are more accurate, and volatility surfaces that more closely reflect market conditions.

Derivatives pricing is often the hinge on which profit is made or lost in financial institutions, making accuracy of utmost importance. This book will help risk managers, traders, portfolio managers, quants, academics and other professionals better understand the Heston model and its extensions, in a writing style that is clear, concise, transparent and easy to understand. For better pricing accuracy, The Heston Model and Its Extensions in VBA is a crucial resource for producing more accurate model outputs such as prices, hedge ratios, volatilities, and graphs.




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


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


Chapter 3: Derivations Using the Fourier Transform

Derivation of Gatheral (2006)

Attari (2004) Representation

Carr and Madan (1999) Representation


Chapter 4: The Fundamental Transform for Pricing Options

The Payoff Transform

Option Prices Using Parseval’s Identity

Volatility of Volatility Series Expansion


Chapter 5: Numerical Integration Schemes

The Integrand in Numerical Integration

Newton-Cotes Formulas

Gaussian Quadrature

Integration Limits, Multi-Domain Integration, and Kahl and Jäckel Transformation

Illustration of Numerical Integration

Fast Fourier Transform

Fractional Fast Fourier Transform


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


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


Chapter 8: American Options

Least-Squares Monte Carlo

The Explicit Method

Beliaeva-Nawalkha Bivariate Tree

Medvedev-Scaillet Expansion

Chiarella and Ziogas American Call


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

Elices Model

Benhamou-Miri-Gobet Model

Black-Scholes Derivatives


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


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


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



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