Wipplinger, Evert

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Financ Mark Portfolio Manag (2008) 22: 93–94DOI 10.1007/s11408-007-0072-4B O O K R E V I E WJim Gatheral: The volatility surface, a practitioner’sguideISBN 0-471-79251-9, Wiley (2006), 179 pages, approx. 100 CHFEvert WipplingerPublished online: 10 January 2008© Swiss Society for Financial Market Research 2008Gatheral’s book The Volatility Surface is subtitled A Practitioner’s Guide, but be-ware! The practitioner for whom the book is meant is one with a mathematical fi-nance background. If you are not interested in an applied mathematical treatment,read no further, as this book will not be to your liking. The book originates in lecturenotes from a course the author taught at New York University. For the most part, theauthor follows the original sources of option pricing theory closely, sometimes lineby line. The added value of the exposition is from aggregating these and directingthe reader to the implications for modeling the volatility surface. Mathematical rigoris not stressed in the presentation as the target audience for the book is expected toalready be familiar with option pricing well beyond Black-Scholes and also knowl-edgeable of the relevant tools from stochastic calculus, partial differential equations,and functional analysis, such as characteristic functions. One of the main topics inthe book is a comparison of the Heston (1993) model and extensions of it that in-clude jumps with local volatility models in terms of the volatility surface of equityoptions. Similarities of the models when pricing plain-vanilla options and the dif-ferent implications for the dynamics of the volatility skew are discussed at severalpoints. The author employs mostly heuristic arguments and analytical relationshipsbetween the models; the latter are sometimes derived from approximations or withlimit arguments.The unique feature of Gatheral’s treatment of the subject is its brevity and theauthor’s focus on using analytic relationships to make his points. For example, Re-bonato’s Volatility and Correlation (2nd ed., 2004) has 836 pages; Gatheral’s bookhas 179. Naturally, Rebonato’s book covers more topics, including equity and fixedE. Wipplinger ()Universität St. Gallen, Rosenbergstr. 52, 9000 St. Gallen, Switzerlande-mail: evert.wipplinger@unisg.ch94 E. Wipplingerincome dynamics and many general empirical relationships, whereas Gatheral’s bookfocuses on the implications of modeling equity volatility surfaces.The author sets up the theoretical framework in the first five chapters, starting witha definition of local variance and relating it to implied and instantaneous variances.The second chapter introduces the Heston model. Chapter 3 further elaborates onthe relationship between local, implied, and instantaneous variance, resulting in anoperationalized representation that is used in the fourth chapter to compare local andstochastic volatility models for a specific parameter set of the Heston model. This firstpart of the book concludes, in Chapter 5, with heuristic empirical arguments makinga case for including jumps when modeling the underlying. The next part of the bookhas a more “applied” nature, but still relies heavily on analytic representations.Chapter 6 deals with simplistic models on credit risk and illustrates the effect ofcredit spreads on the volatility skew. In Chapters 7 and 8, the author reverts to hismain topic of comparing stochastic and local volatility models. His insight is thatwhile the shape of the volatility surface can be reproduced by many models, the im-plicit dynamics resulting from local volatility models are unrealistic. These resultsare applied to barrier options and exotic forward-starting options to illustrate the pre-vious sections. The final chapter deals with pricing volatility derivatives, which areincreasingly popular with market participants. Gatheral reviews the analytic formu-las for the valuation of volatility and variance swaps and briefly discusses hedgingissues.What I found lacking in this book are further references, especially in the em-pirical and credit risk sections. I realize that providing a comprehensive literaturereview is not the purpose of Gatheral’s book and certainly would have increased itslength; however, a brief paragraph at the end of each chapter citing additional rele-vant literature would have gone a long way toward providing the reader with more ofa reference book on volatility surface models. Overall, this book will not replace thestack of papers the reader has likely already compiled on the subject. Even so, I dorecommend this book to those familiar with its topic and who want to refresh theirknowledge of or look up economic implications and implementation issues regardingvarious models for the volatility surface.

Jim Gatheral: The volatility surface, apractitioner's guide: ISBN 0-471-79251-9, Wiley (2006), 179 pages, approx. 100 CHF

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Jim Gatheral: The volatility surface, apractitioner's guide: ISBN 0-471-79251-9, Wiley (2006), 179 pages, approx. 100 CHF

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