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.

List of contents

Foreword xi
 
Preface xiii
 
Acknowledgments xv
 
About This Book xvii
 
VBA Library for Complex Numbers xix
 
Chapter 1 The Heston Model for European Options 1
 
Model Dynamics 1
 
The Heston European Call Price 2
 
Dividend Yield and the Put Price 8
 
Consolidating the Integrals 9
 
Black-Scholes as a Special Case 10
 
Conclusion 12
 
Chapter 2 Integration Issues, Parameter Effects, and Variance Modeling 13
 
Remarks on the Characteristic Functions 14
 
Problems with the Integrand 16
 
The Little Heston Trap 18
 
Effect of the Heston Parameters 20
 
Variance Modeling in the Heston Model 26
 
Moment Explosions 38
 
Bounds on Implied Volatility Slope 40
 
Conclusion 42
 
Chapter 3 Derivations Using the Fourier Transform 45
 
Derivation of Gatheral (2006) 46
 
Attari (2004) Representation 47
 
Carr and Madan (1999) Representation 49
 
Conclusion 61
 
Chapter 4 The Fundamental Transform for Pricing Options 63
 
The Payoff Transform 64
 
Option Prices Using Parseval's Identity 70
 
Volatility of Volatility Series Expansion 75
 
Conclusion 81
 
Chapter 5 Numerical Integration Schemes 83
 
The Integrand in Numerical Integration 84
 
Newton-Cotes Formulas 85
 
Gaussian Quadrature 90
 
Integration Limits, Multidomain Integration, and Kahl and Jäckel Transformation 98
 
Illustration of Numerical Integration 103
 
Fast Fourier Transform 106
 
Fractional Fast Fourier Transform 108
 
Conclusion 114
 
Chapter 6 Parameter Estimation 115
 
Estimation Using Loss Functions 116
 
Speeding Up the Estimation 126
 
Differential Evolution 128
 
Maximum Likelihood Estimation 132
 
Risk-Neutral Density and Arbitrage-Free Volatility Surface 135
 
Conclusion 140
 
Chapter 7 Simulation in the Heston Model 143
 
General Setup 144
 
Euler Scheme 146
 
Milstein Scheme 147
 
Implicit Milstein Scheme 149
 
Transformed Volatility Scheme 152
 
Balanced, Pathwise, and IJK Schemes 155
 
Quadratic-Exponential Scheme 157
 
Alfonsi Scheme for the Variance 161
 
Moment-Matching Scheme 165
 
Conclusion 167
 
Chapter 8 American Options 169
 
Least-Squares Monte Carlo 169
 
The Explicit Method 174
 
Beliaeva-Nawalkha Bivariate Tree 178
 
Medvedev-Scaillet Expansion 191
 
Chiarella and Ziogas American Call 200
 
Conclusion 208
 
Chapter 9 Time-Dependent Heston Models 209
 
Generalization of the Riccati Equation 209
 
Bivariate Characteristic Function 210
 
Linking the Bivariate CF and the General Riccati Equation 212
 
Mikhailov and Nögel Model 214
 
Elices Model 219
 
Benhamou-Miri-Gobet Model 223
 
Black-Scholes Derivatives 231
 
Conclusion 232
 
Chapter 10 Methods for Finite Differences 235
 
The PDE in Terms of an Operator 236
 
Building Grids 236
 
Finite Difference Approximation of Derivatives 239
 
Boundary Conditions for the PDE 240
 
The Weighted Method 241
 
Explicit Scheme 248
 
ADI Schemes 251
 
Conclusion 256
 
Chapter 11 The Heston Greeks 257
 
Analytic Expressions for European Greeks 258
 
Finite Differences for the Greeks 263
 
Numerical Implementation of the Greeks 264
 
Greeks under the Attari and Carr-Madan Form

About the author

FABRICE DOUGLAS ROUAH was a quantitative analyst who specialized in financial modeling of derivatives for pricing and risk management at Sapient Global Markets, a global consultancy. Prior to joining Sapient, Rouah worked at State Street Corporation and McGill University. He is the coauthor and/or coeditor of five books on hedge funds, commodity trading advisors, and option pricing. Rouah holds a PhD in finance and an MSc in statistics from McGill University, and a BSc in applied mathematics from Concordia University.

Summary

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.

Product details

• Authors: Steven L. Heston, Rouah, F Rouah, Fabrice D Rouah, Fabrice D. Rouah, Fabrice Douglas Rouah
• Assisted by: Steven L. Heston (Foreword), Heston Steven L. (Foreword)
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Paperback / Softback
• Released: 29.05.2015
• EAN: 9781119003304
• ISBN: 978-1-119-00330-4
• No. of pages: 352
• Series: Wiley Finance Editions; The Wiley Finance Series; Wiley Finance; Wiley Finance Editions
• Subjects: Social sciences, law, business > Business > Business administration; Finanzwesen, Finance & Investments, Finanz- u. Anlagewesen, Spezialthemen Finanz- u. Anlagewesen, Finance & Investments Special Topics