Fabrice D. Rouah

The Heston Model and Its Extensions in VBA

Mitarbeit: Heston, Steven L.

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Wiley Finance Series
• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 352
• Erscheinungstermin: 27. April 2015
• Englisch
• Abmessung: 254mm x 178mm x 19mm
• Gewicht: 655g
• ISBN-13: 9781119003304
• ISBN-10: 111900330X
• Artikelnr.: 41243777

Autorenporträt

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.

Inhaltsangabe

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 Formulations 267
Greeks under the Lewis Formulations 273 Greeks Using the FFT and FRFT 276
American Greeks Using Simulation 279 American Greeks Using the Explicit
Method 281 American Greeks from Medvedev and Scaillet 284 Conclusion 285
Chapter 12 The Double Heston Model 287 Multidimensional Feynman-Kac Theorem
288 Double Heston Call Price 288 Double Heston Greeks 292 Parameter
Estimation 297 Simulation in the Double Heston Model 301 American Options
in the Double Heston Model 306 Conclusion 308 Bibliography 309 About the
Website 317 Index 319