{"product_id":"the-volatility-surface-isbn-9780471792512","title":"The Volatility Surface","description":"Praise for The Volatility Surface\u003cbr\u003e \u003cbr\u003e \u003cbr\u003e \"I'm thrilled by the appearance of Jim Gatheral's new book The Volatility Surface. The literature on stochastic volatility is vast, but difficult to penetrate and use. Gatheral's book, by contrast, is accessible and practical. It successfully charts a middle ground between specific examples and general models--achieving remarkable clarity without giving up sophistication, depth, or breadth.\"\u003cbr\u003e --Robert V. Kohn, Professor of Mathematics and Chair, Mathematical Finance Committee, Courant Institute of Mathematical Sciences, New York University\u003cbr\u003e \u003cbr\u003e \"Concise yet comprehensive, equally attentive to both theory and phenomena, this book provides an unsurpassed account of the peculiarities of the implied volatility surface, its consequences for pricing and hedging, and the theories that struggle to explain it.\"\u003cbr\u003e --Emanuel Derman, author of My Life as a Quant\u003cbr\u003e \u003cbr\u003e \"Jim Gatheral is the wiliest practitioner in the business. This very fine book is an outgrowth of the lecture notes prepared for one of the most popular classes at NYU's esteemed Courant Institute. The topics covered are at the forefront of research in mathematical finance and the author's treatment of them is simply the best available in this form.\"\u003cbr\u003e --Peter Carr, PhD, head of Quantitative Financial Research, Bloomberg LP Director of the Masters Program in Mathematical Finance, New York University\u003cbr\u003e \u003cbr\u003e \"Jim Gatheral is an acknowledged master of advanced modeling for derivatives. In The Volatility Surface he reveals the secrets of dealing with the most important but most elusive of financial quantities, volatility.\"\u003cbr\u003e --Paul Wilmott, author and mathematician\u003cbr\u003e \u003cbr\u003e \"As a teacher in the field of mathematical finance, I welcome Jim Gatheral's book as a significant development. Written by a Wall Street practitioner with extensive market and teaching experience, The Volatility Surface gives students access to a level of knowledge on derivatives which was not previously available. I strongly recommend it.\"\u003cbr\u003e --Marco Avellaneda, Director, Division of Mathematical Finance Courant Institute, New York University\u003cbr\u003e \u003cbr\u003e \"Jim Gatheral could not have written a better book.\"\u003cbr\u003e --Bruno Dupire, winner of the 2006 Wilmott Cutting Edge Research Award Quantitative Research, Bloomberg LP \u003cp\u003eList of Figures xiii\u003c\/p\u003e \u003cp\u003eList of Tables xix\u003c\/p\u003e \u003cp\u003eForeword xxi\u003c\/p\u003e \u003cp\u003ePreface xxiii\u003c\/p\u003e \u003cp\u003eAcknowledgments xxvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 1 Stochastic Volatility and Local Volatility 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eStochastic Volatility 1\u003c\/p\u003e \u003cp\u003eDerivation of the Valuation Equation 4\u003c\/p\u003e \u003cp\u003eLocal Volatility 7\u003c\/p\u003e \u003cp\u003eHistory 7\u003c\/p\u003e \u003cp\u003eA Brief Review of Dupire’s Work 8\u003c\/p\u003e \u003cp\u003eDerivation of the Dupire Equation 9\u003c\/p\u003e \u003cp\u003eLocal Volatility in Terms of Implied Volatility 11\u003c\/p\u003e \u003cp\u003eSpecial Case: No Skew 13\u003c\/p\u003e \u003cp\u003eLocal Variance as a Conditional Expectation of Instantaneous Variance 13\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 2 The Heston Model 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Process 15\u003c\/p\u003e \u003cp\u003eThe Heston Solution for European Options 16\u003c\/p\u003e \u003cp\u003eA Digression: The Complex Logarithm in the Integration (2.13) 19\u003c\/p\u003e \u003cp\u003eDerivation of the Heston Characteristic Function 20\u003c\/p\u003e \u003cp\u003eSimulation of the Heston Process 21\u003c\/p\u003e \u003cp\u003eMilstein Discretization 22\u003c\/p\u003e \u003cp\u003eSampling from the Exact Transition Law 23\u003c\/p\u003e \u003cp\u003eWhy the Heston Model Is so Popular 24\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 3 The Implied Volatility Surface 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eGetting Implied Volatility from Local Volatilities 25\u003c\/p\u003e \u003cp\u003eModel Calibration 25\u003c\/p\u003e \u003cp\u003eUnderstanding Implied Volatility 26\u003c\/p\u003e \u003cp\u003eLocal Volatility in the Heston Model 31\u003c\/p\u003e \u003cp\u003eAnsatz 32\u003c\/p\u003e \u003cp\u003eImplied Volatility in the Heston Model 33\u003c\/p\u003e \u003cp\u003eThe Term Structure of Black-Scholes Implied Volatility in the Heston Model 34\u003c\/p\u003e \u003cp\u003eThe Black-Scholes Implied Volatility Skew in the Heston Model 35\u003c\/p\u003e \u003cp\u003eThe SPX Implied Volatility Surface 36\u003c\/p\u003e \u003cp\u003eAnother Digression: The SVI Parameterization 37\u003c\/p\u003e \u003cp\u003eA Heston Fit to the Data 40\u003c\/p\u003e \u003cp\u003eFinal Remarks on SV Models and Fitting the Volatility Surface 42\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 4 The Heston-Nandi Model 43\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eLocal Variance in the Heston-Nandi Model 43\u003c\/p\u003e \u003cp\u003eA Numerical Example 44\u003c\/p\u003e \u003cp\u003eThe Heston-Nandi Density 45\u003c\/p\u003e \u003cp\u003eComputation of Local Volatilities 45\u003c\/p\u003e \u003cp\u003eComputation of Implied Volatilities 46\u003c\/p\u003e \u003cp\u003eDiscussion of Results 49\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 5 Adding Jumps 50\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eWhy Jumps are Needed 50\u003c\/p\u003e \u003cp\u003eJump Diffusion 52\u003c\/p\u003e \u003cp\u003eDerivation of the Valuation Equation 52\u003c\/p\u003e \u003cp\u003eUncertain Jump Size 54\u003c\/p\u003e \u003cp\u003eCharacteristic Function Methods 56\u003c\/p\u003e \u003cp\u003eLévy Processes 56\u003c\/p\u003e \u003cp\u003eExamples of Characteristic Functions for Specific Processes 57\u003c\/p\u003e \u003cp\u003eComputing Option Prices from the Characteristic Function 58\u003c\/p\u003e \u003cp\u003eProof of (5.6) 58\u003c\/p\u003e \u003cp\u003eComputing Implied Volatility 60\u003c\/p\u003e \u003cp\u003eComputing the At-the-Money Volatility Skew 60\u003c\/p\u003e \u003cp\u003eHow Jumps Impact the Volatility Skew 61\u003c\/p\u003e \u003cp\u003eStochastic Volatility Plus Jumps 65\u003c\/p\u003e \u003cp\u003eStochastic Volatility Plus Jumps in the Underlying Only (SVJ) 65\u003c\/p\u003e \u003cp\u003eSome Empirical Fits to the SPX Volatility Surface 66\u003c\/p\u003e \u003cp\u003eStochastic Volatility with Simultaneous Jumps in Stock Price and Volatility (SVJJ) 68\u003c\/p\u003e \u003cp\u003eSVJ Fit to the September 15, 2005, SPX Option Data 71\u003c\/p\u003e \u003cp\u003eWhy the SVJ Model Wins 73\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 6 Modeling Default Risk 74\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMerton’s Model of Default 74\u003c\/p\u003e \u003cp\u003eIntuition 75\u003c\/p\u003e \u003cp\u003eImplications for the Volatility Skew 76\u003c\/p\u003e \u003cp\u003eCapital Structure Arbitrage 77\u003c\/p\u003e \u003cp\u003ePut-Call Parity 77\u003c\/p\u003e \u003cp\u003eThe Arbitrage 78\u003c\/p\u003e \u003cp\u003eLocal and Implied Volatility in the Jump-to-Ruin Model 79\u003c\/p\u003e \u003cp\u003eThe Effect of Default Risk on Option Prices 82\u003c\/p\u003e \u003cp\u003eThe CreditGrades Model 84\u003c\/p\u003e \u003cp\u003eModel Setup 84\u003c\/p\u003e \u003cp\u003eSurvival Probability 85\u003c\/p\u003e \u003cp\u003eEquity Volatility 86\u003c\/p\u003e \u003cp\u003eModel Calibration 86\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 7 Volatility Surface Asymptotics 87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eShort Expirations 87\u003c\/p\u003e \u003cp\u003eThe Medvedev-Scaillet Result 89\u003c\/p\u003e \u003cp\u003eThe SABR Model 91\u003c\/p\u003e \u003cp\u003eIncluding Jumps 93\u003c\/p\u003e \u003cp\u003eCorollaries 94\u003c\/p\u003e \u003cp\u003eLong Expirations: Fouque, Papanicolaou, and Sircar 95\u003c\/p\u003e \u003cp\u003eSmall Volatility of Volatility: Lewis 96\u003c\/p\u003e \u003cp\u003eExtreme Strikes: Roger Lee 97\u003c\/p\u003e \u003cp\u003eExample: Black-Scholes 99\u003c\/p\u003e \u003cp\u003eStochastic Volatility Models 99\u003c\/p\u003e \u003cp\u003eAsymptotics in Summary 100\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 8 Dynamics of the Volatility Surface 101\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eDynamics of the Volatility Skew under Stochastic Volatility 101\u003c\/p\u003e \u003cp\u003eDynamics of the Volatility Skew under Local Volatility 102\u003c\/p\u003e \u003cp\u003eStochastic Implied Volatility Models 103\u003c\/p\u003e \u003cp\u003eDigital Options and Digital Cliquets 103\u003c\/p\u003e \u003cp\u003eValuing Digital Options 104\u003c\/p\u003e \u003cp\u003eDigital Cliquets 104\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 9 Barrier Options 107\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eDefinitions 107\u003c\/p\u003e \u003cp\u003eLimiting Cases 108\u003c\/p\u003e \u003cp\u003eLimit Orders 108\u003c\/p\u003e \u003cp\u003eEuropean Capped Calls 109\u003c\/p\u003e \u003cp\u003eThe Reflection Principle 109\u003c\/p\u003e \u003cp\u003eThe Lookback Hedging Argument 112\u003c\/p\u003e \u003cp\u003eOne-Touch Options Again 113\u003c\/p\u003e \u003cp\u003ePut-Call Symmetry 113\u003c\/p\u003e \u003cp\u003eQuasiStatic Hedging and Qualitative Valuation 114\u003c\/p\u003e \u003cp\u003eOut-of-the-Money Barrier Options 114\u003c\/p\u003e \u003cp\u003eOne-Touch Options 115\u003c\/p\u003e \u003cp\u003eLive-Out Options 116\u003c\/p\u003e \u003cp\u003eLookback Options 117\u003c\/p\u003e \u003cp\u003eAdjusting for Discrete Monitoring 117\u003c\/p\u003e \u003cp\u003eDiscretely Monitored Lookback Options 119\u003c\/p\u003e \u003cp\u003eParisian Options 120\u003c\/p\u003e \u003cp\u003eSome Applications of Barrier Options 120\u003c\/p\u003e \u003cp\u003eLadders 120\u003c\/p\u003e \u003cp\u003eRanges 120\u003c\/p\u003e \u003cp\u003eConclusion 121\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 10 Exotic Cliquets 122\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eLocally Capped Globally Floored Cliquet 122\u003c\/p\u003e \u003cp\u003eValuation under Heston and Local Volatility Assumptions 123\u003c\/p\u003e \u003cp\u003ePerformance 124\u003c\/p\u003e \u003cp\u003eReverse Cliquet 125\u003c\/p\u003e \u003cp\u003eValuation under Heston and Local Volatility Assumptions 126\u003c\/p\u003e \u003cp\u003ePerformance 127\u003c\/p\u003e \u003cp\u003eNapoleon 127\u003c\/p\u003e \u003cp\u003eValuation under Heston and Local Volatility Assumptions 128\u003c\/p\u003e \u003cp\u003ePerformance 130\u003c\/p\u003e \u003cp\u003eInvestor Motivation 130\u003c\/p\u003e \u003cp\u003eMore on Napoleons 131\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 11 Volatility Derivatives 133\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSpanning Generalized European Payoffs 133\u003c\/p\u003e \u003cp\u003eExample: European Options 134\u003c\/p\u003e \u003cp\u003eExample: Amortizing Options 135\u003c\/p\u003e \u003cp\u003eThe Log Contract 135\u003c\/p\u003e \u003cp\u003eVariance and Volatility Swaps 136\u003c\/p\u003e \u003cp\u003eVariance Swaps 137\u003c\/p\u003e \u003cp\u003eVariance Swaps in the Heston Model 138\u003c\/p\u003e \u003cp\u003eDependence on Skew and Curvature 138\u003c\/p\u003e \u003cp\u003eThe Effect of Jumps 140\u003c\/p\u003e \u003cp\u003eVolatility Swaps 143\u003c\/p\u003e \u003cp\u003eConvexity Adjustment in the Heston Model 144\u003c\/p\u003e \u003cp\u003eValuing Volatility Derivatives 146\u003c\/p\u003e \u003cp\u003eFair Value of the Power Payoff 146\u003c\/p\u003e \u003cp\u003eThe Laplace Transform of Quadratic Variation under Zero Correlation 147\u003c\/p\u003e \u003cp\u003eThe Fair Value of Volatility under Zero Correlation 149\u003c\/p\u003e \u003cp\u003eA Simple Lognormal Model 151\u003c\/p\u003e \u003cp\u003eOptions on Volatility: More on Model Independence 154\u003c\/p\u003e \u003cp\u003eListed Quadratic-Variation Based Securities 156\u003c\/p\u003e \u003cp\u003eThe VIX Index 156\u003c\/p\u003e \u003cp\u003eVXB Futures 158\u003c\/p\u003e \u003cp\u003eKnock-on Benefits 160\u003c\/p\u003e \u003cp\u003eSummary 161\u003c\/p\u003e \u003cp\u003ePostscript 162\u003c\/p\u003e \u003cp\u003eBibliography 163\u003c\/p\u003e \u003cp\u003eIndex 169\u003c\/p\u003e “…I do recommend this book…” (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e , Vol. 1118 2007\/20) \u003cp\u003e\u003cb\u003eJIM GATHERAL\u003c\/b\u003e is a Managing Director at Merrill Lynch and also an Adjunct Professor at the Courant Institute of Mathematical Sciences, New York University.Dr. Gatheral obtained a PhD in theoretical physics from Cambridge Universityin 1983. Since then, he has been involved in all of the major derivative product areasas a bookrunner, risk manager, and quantitative analyst in London, Tokyo, and New York. From 1997 to 2005, Dr. Gatheral headed the Equity Quantitative Analytics group at Merrill Lynch. His current research focus is equity market microstructure and algorithmic trading.\u003c\/p\u003e \u003cp\u003eWith a foreword by \u003cb\u003eNassim Nicholas Taleb\u003c\/b\u003e\u003cbr\u003eTaleb is the Dean's Professor in the Sciences of Uncertainty at the University of Massachusetts at Amherst. He is also author of \u003ci\u003eFooled by Randomness: The Hidden Role of Chance in Life and in the Markets\u003c\/i\u003e (Random House, 2005).\u003c\/p\u003e  Understanding the volatility surface is a key objective for both practitioners and academics in the field of finance. Implied volatilities evolve randomly and so models of the volatility surface—which is formed from implied volatilities of all strikes and expirations—need to explicitly reflect this randomness in order to accurately price, trade, and manage the risk of derivative products.\u003cbr\u003e \u003cbr\u003e   \u003cp\u003eAuthor and financial professional Jim Gatheral is intimately familiar with these issues and, in The Volatility Surface, he shares his many years of knowledge and experience to help make sense of it all. Written by a practitionerfor practitioners, The Volatility Surface examines why options are priced as they are and—starting from a powerful representation of implied volatility in terms of a weighted average ofrealized volatilities—explores the implications of various popular models for pricing.\u003c\/p\u003e \u003cp\u003eThe first half of this book focuses on setting up the theoretical framework, while the later chapters are oriented towards practical applications. Informative and accessible, The Volatility Surface:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eContains a detailed derivation of the Heston model and explanations of many other popular models such as SVJ, SVJJ, SABR, and CreditGrades\u003c\/li\u003e \u003cli\u003eDiscusses the characteristics of various types of exotic options from the humble barrier option to the super exotic Napoleon\u003c\/li\u003e \u003cli\u003eExhaustively covers volatility derivatives with elegant and robust presentations of the latest research\u003c\/li\u003e \u003cli\u003eExamines performance of exotic cliquet contracts through in-depth case studies of actual bonds that have already matured\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe purpose of The Volatility Surface is not to just present results, but to provide you with ways of thinking about and solving practical problems that should have many other areas of application. So by the time you finish reading this guide, you'll have a firm understanding of volatility surface modeling as well as a better idea of how you can apply the results of these models to real-world situations.\u003c\/p\u003e \u003cp\u003eFilled with in-depth insights, expert advice, and real-world examples, The Volatility Surface will get you up to speed on the latest theories underlying options pricing as well as familiarize you with the history and practice of trading in the equity derivatives markets.\u003c\/p\u003e  \u003cp\u003e\"I'm thrilled by the appearance of Jim Gatheral's new book \u003ci\u003eThe Volatility Surface.\u003c\/i\u003e The literature on stochastic volatility is vast, but difficult to penetrate and use. Gatheral's book, by contrast, is accessible and practical. It successfully charts a middle ground between specific examples and general models—achieving remarkable clarity without giving up sophistication, depth, or breadth.\" \u003cb\u003e—Robert V. Kohn, Professor of Mathematics and Chair, Mathematical Finance Committee, Courant Institute of Mathematical Sciences, New York University\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\"Concise yet comprehensive, equally attentive to both theory and phenomena, this book provides an unsurpassed account of the peculiarities of the implied volatility surface, its consequences for pricing and hedging, and the theories that struggle to explain it.\" \u003cb\u003e—Emanuel Derman, author of\u003ci\u003e My Life as a Quant\u003c\/i\u003e\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\"Jim Gatheral is the wiliest practitioner in the business. This very fine book is an outgrowth of the lecture notes prepared for one of the most popular classes at NYU's esteemed Courant Institute. The topics covered are at the forefront of research in mathematical finance and the author's treatment of them is simply the best available in this form.\" \u003cb\u003e—Peter Carr, PhD, head of Quantitative Financial Research, Bloomberg LP Director of the Masters Program in Mathematical Finance, New York University\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\"Jim Gatheral is an acknowledged master of advanced modeling for derivatives. In \u003ci\u003eThe Volatility Surface\u003c\/i\u003e he reveals the secrets of dealing with the most important but most elusive of financial quantities, volatility.\" \u003cb\u003e—Paul Wilmott, author and mathematician\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\"As a teacher in the field of mathematical finance, I welcome Jim Gatheral's book as a significant development. Written by a Wall Street practitioner with extensive market and teaching experience, \u003ci\u003eThe Volatility Surface\u003c\/i\u003e gives students access to a level of knowledge on derivatives which was not previously available. I strongly recommend it.\" \u003cb\u003e—Marco Avellaneda, Director, Division of Mathematical Finance Courant Institute, New York University\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\"Jim Gatheral could not have written a better book.\" \u003cb\u003e—Bruno Dupire, winner of the 2006 Wilmott Cutting Edge Research Award Quantitative Research, Bloomberg LP\u003c\/b\u003e\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47990364471525,"sku":"NP9780471792512","price":73.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471792512.jpg?v=1761787525","url":"https:\/\/k12savings.com\/es\/products\/the-volatility-surface-isbn-9780471792512","provider":"K12savings","version":"1.0","type":"link"}