• Produktbild: The Heston Model and its Extensions in Matlab and C#
  • Produktbild: The Heston Model and its Extensions in Matlab and C#

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

03.09.2013

Verlag

John Wiley & Sons

Seitenzahl

432

Maße (L/B/H)

25.4/17.8/2.3 cm

Gewicht

748 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-118-54825-7

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

03.09.2013

Verlag

John Wiley & Sons

Seitenzahl

432

Maße (L/B/H)

25.4/17.8/2.3 cm

Gewicht

748 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-118-54825-7

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: The Heston Model and its Extensions in Matlab and C#
  • Produktbild: The Heston Model and its Extensions in Matlab and C#
  • Foreword ix

    Preface xi

    Acknowledgments xiii

    CHAPTER 1 The Heston Model for European Options 1

    Model Dynamics 1

    The European Call Price 4

    The Heston PDE 5

    Obtaining the Heston Characteristic Functions 10

    Solving the Heston Riccati Equation 12

    Dividend Yield and the Put Price 17

    Consolidating the Integrals 18

    Black-Scholes as a Special Case 19

    Summary of the Call Price 22

    Conclusion 23

    CHAPTER 2 Integration Issues, Parameter Effects, and Variance Modeling 25

    Remarks on the Characteristic Functions 25

    Problems With the Integrand 29

    The Little Heston Trap 31

    Effect of the Heston Parameters 34

    Variance Modeling in the Heston Model 43

    Moment Explosions 56

    Bounds on Implied Volatility Slope 57

    Conclusion 61

    CHAPTER 3 Derivations Using the Fourier Transform 63

    The Fourier Transform 63

    Recovery of Probabilities With Gil-Pelaez Fourier Inversion 65

    Derivation of Gatheral (2006) 67

    Attari (2004) Representation 69

    Carr and Madan (1999) Representation 73

    Bounds on the Carr-Madan Damping Factor and Optimal Value 76

    The Carr-Madan Representation for Puts 82

    The Representation for OTM Options 84

    Conclusion 89

    CHAPTER 4 The Fundamental Transform for Pricing Options 91

    The Payoff Transform 91

    The Fundamental Transform and the Option Price 92

    The Fundamental Transform for the Heston Model 95

    Option Prices Using Parseval's Identity 100

    Volatility of Volatility Series Expansion 108

    Conclusion 113

    CHAPTER 5 Numerical Integration Schemes 115

    The Integrand in Numerical Integration 116

    Newton-Cotes Formulas 116

    Gaussian Quadrature 121

    Integration Limits and Kahl and J ¨ ackel Transformation 130

    Illustration of Numerical Integration 136

    Fast Fourier Transform 137

    Fractional Fast Fourier Transform 141

    Conclusion 145

    CHAPTER 6 Parameter Estimation 147

    Estimation Using Loss Functions 147

    Speeding up the Estimation 158

    Differential Evolution 162

    Maximum Likelihood Estimation 166

    Risk-Neutral Density and Arbitrage-Free Volatility Surface 170

    Conclusion 175

    CHAPTER 7 Simulation in the Heston Model 177

    General Setup 177

    Euler Scheme 179

    Milstein Scheme 181

    Milstein Scheme for the Heston Model 183

    Implicit Milstein Scheme 185

    Transformed Volatility Scheme 188

    Balanced, Pathwise, and IJK Schemes 191

    Quadratic-Exponential Scheme 193

    Alfonsi Scheme for the Variance 198

    Moment Matching Scheme 201

    Conclusion 202

    CHAPTER 8 American Options 205

    Least-Squares Monte Carlo 205

    The Explicit Method 213

    Beliaeva-Nawalkha Bivariate Tree 217

    Medvedev-Scaillet Expansion 228

    Chiarella and Ziogas American Call 253

    Conclusion 261

    CHAPTER 9 Time-Dependent Heston Models 263

    Generalization of the Riccati Equation 263

    Bivariate Characteristic Function 264

    Linking the Bivariate CF and the General Riccati Equation 269

    Mikhailov and No¨ gel Model 271

    Elices Model 278

    Benhamou-Miri-Gobet Model 285

    Black-Scholes Derivatives 299

    Conclusion 300

    CHAPTER 10 Methods for Finite Differences 301

    The PDE in Terms of an Operator 301

    Building Grids 302

    Finite Difference Approximation of Derivatives 303

    The Weighted Method 306

    Boundary Conditions for the PDE 315

    Explicit Scheme 316

    ADI Schemes 321

    Conclusion 325

    CHAPTER 11 The Heston Greeks 327

    Analytic Expressions for European Greeks 327

    Finite Differences for the Greeks 332

    Numerical Implementation of the Greeks 333

    Greeks Under the Attari and Carr-Madan Formulations 339

    Greeks Under the Lewis Formulations 343

    Greeks Using the FFT and FRFT 345

    American Greeks Using Simulation 346

    American Greeks Using the Explicit Method 349

    American Greeks from Medvedev and Scaillet 352

    Conclusion 354

    CHAPTER 12 The Double Heston Model 357

    Multi-Dimensional Feynman-KAC Theorem 357

    Double Heston Call Price 358

    Double Heston Greeks 363

    Parameter Estimation 368

    Simulation in the Double Heston Model 373

    American Options in the Double Heston Model 380

    Conclusion 382

    Bibliography 383

    About the Website 391

    Index 397