{"product_id":"the-heston-model-and-its-extensions-in-matlab-and-c-website-isbn-9781118548257","title":"The Heston Model and its Extensions in Matlab and C#, + Website","description":"\u003cb\u003eTap into the power of the most popular stochastic volatility model for pricing equity derivatives\u003c\/b\u003e  \u003cp\u003eSince 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.\u003c\/p\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA groundbreaking book dedicated to the exploration of the Heston model—a popular model for pricing equity derivatives\u003c\/li\u003e \u003cli\u003eIncludes a companion website, which explores the Heston model and its extensions all coded in Matlab and C#\u003c\/li\u003e \u003cli\u003eWritten by Fabrice Douglas Rouah a quantitative analyst who specializes in financial modeling for derivatives for pricing and risk management\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eEngaging 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.\u003c\/p\u003e  \u003cp\u003eForeword ix\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgments xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 1 The Heston Model for European Options 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eModel Dynamics 1\u003c\/p\u003e \u003cp\u003eThe European Call Price 4\u003c\/p\u003e \u003cp\u003eThe Heston PDE 5\u003c\/p\u003e \u003cp\u003eObtaining the Heston Characteristic Functions 10\u003c\/p\u003e \u003cp\u003eSolving the Heston Riccati Equation 12\u003c\/p\u003e \u003cp\u003eDividend Yield and the Put Price 17\u003c\/p\u003e \u003cp\u003eConsolidating the Integrals 18\u003c\/p\u003e \u003cp\u003eBlack-Scholes as a Special Case 19\u003c\/p\u003e \u003cp\u003eSummary of the Call Price 22\u003c\/p\u003e \u003cp\u003eConclusion 23\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 2 Integration Issues, Parameter Effects, and Variance Modeling 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eRemarks on the Characteristic Functions 25\u003c\/p\u003e \u003cp\u003eProblems With the Integrand 29\u003c\/p\u003e \u003cp\u003eThe Little Heston Trap 31\u003c\/p\u003e \u003cp\u003eEffect of the Heston Parameters 34\u003c\/p\u003e \u003cp\u003eVariance Modeling in the Heston Model 43\u003c\/p\u003e \u003cp\u003eMoment Explosions 56\u003c\/p\u003e \u003cp\u003eBounds on Implied Volatility Slope 57\u003c\/p\u003e \u003cp\u003eConclusion 61\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 3 Derivations Using the Fourier Transform 63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Fourier Transform 63\u003c\/p\u003e \u003cp\u003eRecovery of Probabilities With Gil-Pelaez Fourier Inversion 65\u003c\/p\u003e \u003cp\u003eDerivation of Gatheral (2006) 67\u003c\/p\u003e \u003cp\u003eAttari (2004) Representation 69\u003c\/p\u003e \u003cp\u003eCarr and Madan (1999) Representation 73\u003c\/p\u003e \u003cp\u003eBounds on the Carr-Madan Damping Factor and Optimal Value 76\u003c\/p\u003e \u003cp\u003eThe Carr-Madan Representation for Puts 82\u003c\/p\u003e \u003cp\u003eThe Representation for OTM Options 84\u003c\/p\u003e \u003cp\u003eConclusion 89\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 4 The Fundamental Transform for Pricing Options 91\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Payoff Transform 91\u003c\/p\u003e \u003cp\u003eThe Fundamental Transform and the Option Price 92\u003c\/p\u003e \u003cp\u003eThe Fundamental Transform for the Heston Model 95\u003c\/p\u003e \u003cp\u003eOption Prices Using Parseval’s Identity 100\u003c\/p\u003e \u003cp\u003eVolatility of Volatility Series Expansion 108\u003c\/p\u003e \u003cp\u003eConclusion 113\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 5 Numerical Integration Schemes 115\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Integrand in Numerical Integration 116\u003c\/p\u003e \u003cp\u003eNewton-Cotes Formulas 116\u003c\/p\u003e \u003cp\u003eGaussian Quadrature 121\u003c\/p\u003e \u003cp\u003eIntegration Limits and Kahl and J ¨ ackel Transformation 130\u003c\/p\u003e \u003cp\u003eIllustration of Numerical Integration 136\u003c\/p\u003e \u003cp\u003eFast Fourier Transform 137\u003c\/p\u003e \u003cp\u003eFractional Fast Fourier Transform 141\u003c\/p\u003e \u003cp\u003eConclusion 145\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 6 Parameter Estimation 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eEstimation Using Loss Functions 147\u003c\/p\u003e \u003cp\u003eSpeeding up the Estimation 158\u003c\/p\u003e \u003cp\u003eDifferential Evolution 162\u003c\/p\u003e \u003cp\u003eMaximum Likelihood Estimation 166\u003c\/p\u003e \u003cp\u003eRisk-Neutral Density and Arbitrage-Free Volatility Surface 170\u003c\/p\u003e \u003cp\u003eConclusion 175\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 7 Simulation in the Heston Model 177\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eGeneral Setup 177\u003c\/p\u003e \u003cp\u003eEuler Scheme 179\u003c\/p\u003e \u003cp\u003eMilstein Scheme 181\u003c\/p\u003e \u003cp\u003eMilstein Scheme for the Heston Model 183\u003c\/p\u003e \u003cp\u003eImplicit Milstein Scheme 185\u003c\/p\u003e \u003cp\u003eTransformed Volatility Scheme 188\u003c\/p\u003e \u003cp\u003eBalanced, Pathwise, and IJK Schemes 191\u003c\/p\u003e \u003cp\u003eQuadratic-Exponential Scheme 193\u003c\/p\u003e \u003cp\u003eAlfonsi Scheme for the Variance 198\u003c\/p\u003e \u003cp\u003eMoment Matching Scheme 201\u003c\/p\u003e \u003cp\u003eConclusion 202\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 8 American Options 205\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eLeast-Squares Monte Carlo 205\u003c\/p\u003e \u003cp\u003eThe Explicit Method 213\u003c\/p\u003e \u003cp\u003eBeliaeva-Nawalkha Bivariate Tree 217\u003c\/p\u003e \u003cp\u003eMedvedev-Scaillet Expansion 228\u003c\/p\u003e \u003cp\u003eChiarella and Ziogas American Call 253\u003c\/p\u003e \u003cp\u003eConclusion 261\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 9 Time-Dependent Heston Models 263\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eGeneralization of the Riccati Equation 263\u003c\/p\u003e \u003cp\u003eBivariate Characteristic Function 264\u003c\/p\u003e \u003cp\u003eLinking the Bivariate CF and the General Riccati Equation 269\u003c\/p\u003e \u003cp\u003eMikhailov and No¨ gel Model 271\u003c\/p\u003e \u003cp\u003eElices Model 278\u003c\/p\u003e \u003cp\u003eBenhamou-Miri-Gobet Model 285\u003c\/p\u003e \u003cp\u003eBlack-Scholes Derivatives 299\u003c\/p\u003e \u003cp\u003eConclusion 300\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 10 Methods for Finite Differences 301\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe PDE in Terms of an Operator 301\u003c\/p\u003e \u003cp\u003eBuilding Grids 302\u003c\/p\u003e \u003cp\u003eFinite Difference Approximation of Derivatives 303\u003c\/p\u003e \u003cp\u003eThe Weighted Method 306\u003c\/p\u003e \u003cp\u003eBoundary Conditions for the PDE 315\u003c\/p\u003e \u003cp\u003eExplicit Scheme 316\u003c\/p\u003e \u003cp\u003eADI Schemes 321\u003c\/p\u003e \u003cp\u003eConclusion 325\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 11 The Heston Greeks 327\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAnalytic Expressions for European Greeks 327\u003c\/p\u003e \u003cp\u003eFinite Differences for the Greeks 332\u003c\/p\u003e \u003cp\u003eNumerical Implementation of the Greeks 333\u003c\/p\u003e \u003cp\u003eGreeks Under the Attari and Carr-Madan Formulations 339\u003c\/p\u003e \u003cp\u003eGreeks Under the Lewis Formulations 343\u003c\/p\u003e \u003cp\u003eGreeks Using the FFT and FRFT 345\u003c\/p\u003e \u003cp\u003eAmerican Greeks Using Simulation 346\u003c\/p\u003e \u003cp\u003eAmerican Greeks Using the Explicit Method 349\u003c\/p\u003e \u003cp\u003eAmerican Greeks from Medvedev and Scaillet 352\u003c\/p\u003e \u003cp\u003eConclusion 354\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 12 The Double Heston Model 357\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMulti-Dimensional Feynman-KAC Theorem 357\u003c\/p\u003e \u003cp\u003eDouble Heston Call Price 358\u003c\/p\u003e \u003cp\u003eDouble Heston Greeks 363\u003c\/p\u003e \u003cp\u003eParameter Estimation 368\u003c\/p\u003e \u003cp\u003eSimulation in the Double Heston Model 373\u003c\/p\u003e \u003cp\u003eAmerican Options in the Double Heston Model 380\u003c\/p\u003e \u003cp\u003eConclusion 382\u003c\/p\u003e \u003cp\u003eBibliography 383\u003c\/p\u003e \u003cp\u003eAbout the Website 391\u003c\/p\u003e \u003cp\u003eIndex 397\u003c\/p\u003e \u003cp\u003e\u003cb\u003eFABRICE DOUGLAS ROUAH\u003c\/b\u003e is a quantitative analyst who specializes 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.\u003c\/p\u003e   \u003cp\u003ePraise for \u003ci\u003eThe Heston Model and Its Extensions in Matlab and C#\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\"In his excellent new book, Fabrice Rouah provides a careful presentation of all aspects of the Heston model, with a strong emphasis on getting the model up and running in practice. This highly practical and useful book is recommended for anyone working with stochastic volatility models.\"\u003cbr\u003e \u003cb\u003e—Leif B. G. Andersen,\u003c\/b\u003e Bank of America Merrill Lynch\u003c\/p\u003e \u003cp\u003e\"Without a doubt, Fabrice provides a very valuable contribution to quantitative analysts interested in pricing options with state-of-the art techniques.\"\u003cbr\u003e \u003cb\u003e—Marco Avellaneda,\u003c\/b\u003e New York University\u003c\/p\u003e \u003cp\u003e\"The Heston model is one of the great success stories of academic finance. Rouah's impressive book provides users with all the tools required to implement the Heston model, and wonderfully bridges the gap between academia and practice.\"\u003cbr\u003e \u003cb\u003e—Peter Christoffersen,\u003c\/b\u003e University of Toronto\u003c\/p\u003e \u003cp\u003e\"In this encyclopedic work, the author takes delight in exploring every aspect of the Heston model. Together with its included Matlab and C# code, this book will prove invaluable to anyone interested in option pricing. I highly recommend it.\"\u003cbr\u003e \u003cb\u003e—Jim Gatheral,\u003c\/b\u003e Baruch College author of \u003ci\u003eThe Volatility Surface: A Practitioner's Guide\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\"This is the most extensive work on the Heston model I have seen: derivations, implementations, and discussions. For anyone interested in the Heston model and its variations, this is an important book to have!\"\u003cbr\u003e \u003cb\u003e—Espen Gaarder Haug,\u003c\/b\u003e Norwegian University of Life Sciences author of \u003ci\u003eDerivatives Models on Models\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\"Rouah offers a unique and much needed synthesis of the literature regarding Heston's model of stochastic volatility. The author has accomplished the formidable task of presenting a large body of published academic and industrial research in a coherent, thorough, and very reader-friendly manner.\"\u003cbr\u003e \u003cb\u003e—Andrew Lesniewski,\u003c\/b\u003e DTCC\u003c\/p\u003e \u003cp\u003e\"Beyond Black-Scholes, the Heston model is arguably the most important model in quantitative finance and certainly deserves its own book. Rouah provides here a comprehensive treatment—clearly discussing all the major issues, later extensions, and subtle traps.\"\u003cbr\u003e \u003cb\u003e—Alan L. Lewis,\u003c\/b\u003e PhD, author of \u003ci\u003eOption Valuation Under Stochastic Volatility: With Mathematica Code\u003c\/i\u003e\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47990257484005,"sku":"NP9781118548257","price":141.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118548257.jpg?v=1761787093","url":"https:\/\/k12savings.com\/products\/the-heston-model-and-its-extensions-in-matlab-and-c-website-isbn-9781118548257","provider":"K12savings","version":"1.0","type":"link"}