{"product_id":"the-volatility-smile-isbn-9781118959169","title":"The Volatility Smile","description":"\u003cp\u003e\u003cb\u003eThe Volatility Smile\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Black-Scholes-Merton option model was the greatest innovation of 20th century finance, and remains the most widely applied theory in all of finance. Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically display a curve or skew, which practitioners refer to as the smile, and which the model cannot explain. Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new models that try to reconcile theory with markets.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eThe Volatility Smile\u003c\/i\u003e presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it. It is also a book about the principles of financial valuation and how to apply them. Celebrated author and quant Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and their assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models.\u003c\/p\u003e \u003cp\u003eTopics covered include:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eThe principles of valuation\u003c\/li\u003e \u003cli\u003eStatic and dynamic replication\u003c\/li\u003e \u003cli\u003eThe Black-Scholes-Merton model\u003c\/li\u003e \u003cli\u003eHedging strategies\u003c\/li\u003e \u003cli\u003eTransaction costs\u003c\/li\u003e \u003cli\u003eThe behavior of the volatility smile\u003c\/li\u003e \u003cli\u003eImplied distributions\u003c\/li\u003e \u003cli\u003eLocal volatility models\u003c\/li\u003e \u003cli\u003eStochastic volatility models\u003c\/li\u003e \u003cli\u003eJump-diffusion models\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe first half of the book, Chapters 1 through 13, can serve as a standalone textbook for a course on option valuation and the Black-Scholes-Merton model, presenting the principles of financial modeling, several derivations of the model, and a detailed discussion of how it is used in practice. The second half focuses on the behavior of the volatility smile, and, in conjunction with the first half, can be used for as the basis for a more advanced course.\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgments xiii\u003c\/p\u003e \u003cp\u003eAbout the Authors xv\u003c\/p\u003e \u003cp\u003eCHAPTER 1 Overview 1\u003c\/p\u003e \u003cp\u003eCHAPTER 2 The Principle of Replication 13\u003c\/p\u003e \u003cp\u003eCHAPTER 3 Static and Dynamic Replication 37\u003c\/p\u003e \u003cp\u003eCHAPTER 4 Variance Swaps: A Lesson in Replication 57\u003c\/p\u003e \u003cp\u003eCHAPTER 5 The P\u0026amp;L of Hedged Option Strategies in a Black-Scholes-Merton World 85\u003c\/p\u003e \u003cp\u003eCHAPTER 6 The Effect of Discrete Hedging on P\u0026amp;L 105\u003c\/p\u003e \u003cp\u003eCHAPTER 7 The Effect of Transaction Costs on P\u0026amp;L 117\u003c\/p\u003e \u003cp\u003eCHAPTER 8 The Smile: Stylized Facts and Their Interpretation 131\u003c\/p\u003e \u003cp\u003eCHAPTER 9 No-Arbitrage Bounds on the Smile 153\u003c\/p\u003e \u003cp\u003eCHAPTER 10 A Survey of Smile Models 163\u003c\/p\u003e \u003cp\u003eCHAPTER 11 Implied Distributions and Static Replication 175\u003c\/p\u003e \u003cp\u003eCHAPTER 12 Weak Static Replication 203\u003c\/p\u003e \u003cp\u003eCHAPTER 13 The Binomial Model and Its Extensions 227\u003c\/p\u003e \u003cp\u003eCHAPTER 14 Local Volatility Models 249\u003c\/p\u003e \u003cp\u003eCHAPTER 15 Consequences of Local Volatility Models 265\u003c\/p\u003e \u003cp\u003eCHAPTER 16 Local Volatility Models: Hedge Ratios and Exotic Option Values 289\u003c\/p\u003e \u003cp\u003eCHAPTER 17 Some Final Remarks on Local Volatility Models 303\u003c\/p\u003e \u003cp\u003eCHAPTER 18 Patterns of Volatility Change 309\u003c\/p\u003e \u003cp\u003eCHAPTER 19 Introducing Stochastic Volatility Models 319\u003c\/p\u003e \u003cp\u003eCHAPTER 20 Approximate Solutions to Some Stochastic Volatility Models 337\u003c\/p\u003e \u003cp\u003eCHAPTER 21 Stochastic Volatility Models: The Smile for Zero Correlation 353\u003c\/p\u003e \u003cp\u003eCHAPTER 22 Stochastic Volatility Models: The Smile with Mean Reversion and Correlation 369\u003c\/p\u003e \u003cp\u003eCHAPTER 23 Jump-Diffusion Models of the Smile: Introduction 383\u003c\/p\u003e \u003cp\u003eCHAPTER 24 The Full Jump-Diffusion Model 395\u003c\/p\u003e \u003cp\u003eEpilogue 417\u003c\/p\u003e \u003cp\u003eAPPENDIX A Some Useful Derivatives of the Black-Scholes-Merton Model 419\u003c\/p\u003e \u003cp\u003eAPPENDIX B Backward Itoˆ Integrals 421\u003c\/p\u003e \u003cp\u003eAPPENDIX C Variance Swap Piecewise-Linear Replication 431\u003c\/p\u003e \u003cp\u003eAnswers to End-of-Chapter Problems 433\u003c\/p\u003e \u003cp\u003eReferences 497\u003c\/p\u003e \u003cp\u003eIndex 501\u003c\/p\u003e \u003cp\u003e\u003cb\u003eEMANUEL DERMAN\u003c\/b\u003e is a professor at Columbia University, where he directs its financial engineering program. He is the author of \u003ci\u003eMy Life as a Quant\u003c\/i\u003e and \u003ci\u003eModels.Behaving.Badly\u003c\/i\u003e.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eMICHAEL B. MILLER\u003c\/b\u003e is the founder and CEO of Northstar Risk Corp. He is the author of \u003ci\u003eMathematics and Statistics for Financial Risk Management, Second Edition.\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eThe Volatility Smile\u003c\/i\u003e provides an accessible account of both the classic Black-Scholes-Merton option model and the newer extensions of the model that have been developed over the past forty years. In contrast to textbooks that accentuate formality over intuition and understanding, \u003ci\u003eThe Volatility Smile\u003c\/i\u003e explores both the ideas and the mathematics behind the models, walking a middle line between the rigor of the academic world and the practical insights of the trading desk. Based on a clear formulation of the principles of financial modeling, \u003ci\u003eThe Volatility Smile\u003c\/i\u003e is also a book about how to evaluate and build financial models.\u003c\/p\u003e \u003cp\u003ePrior to the 1987 global stock market crash, the Black-Scholes-Merton option valuation model seemed to describe option markets reasonably well. Since the crash, however, equity index option markets have displayed a persistent volatility smile, in blatant disagreement with the Black-Scholes-Merton model. Quants around the world have labored over the preceding decades to extend the Black-Scholes-Merton model to accommodate this anomaly.\u003c\/p\u003e \u003cp\u003eGood financial models begin not with mathematics but with an understanding of the behavior of securities and markets. The first half of this book therefore focuses on the theory of option valuation, a study of the Black-Scholes-Merton model, illustrations of how to make practical use of it, and a discussion of its limitations. The second half provides an analysis of the empirical behavior of the volatility smile, and a detailed account of multiple ways in which the Black-Scholes-Merton model can be extended so as to rectify its inadequacies. In particular, the book provides a detailed account of the local volatility model, stochastic volatility models, and jump-diffusion.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eThe Black-Scholes-Merton option model was the greatest innovation of twentieth century finance,\u003c\/b\u003e and remains the most widely applied theory in all of finance. Nevertheless, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatility against strike will typically display a curve or smile, which the model cannot explain. \u003c\/p\u003e\u003cp\u003eOption valuation is not a solved problem, and the past forty years have witnessed an abundance of new ideas and models that try to reconcile theory with markets. Beginning with the principles of financial valuation, \u003ci\u003eThe Volatility Smile\u003c\/i\u003e presents a unique and unified treatment of the Black-Scholes-Merton option model and the more advanced models that have replaced it. Celebrated author, quant, and co-originator of the local volatility model Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and the consequences of different assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models.  Key features: \u003c\/p\u003e\u003cul\u003e \u003cli\u003eThe principles of valuation\u003c\/li\u003e \u003cli\u003eThe Black-Scholes-Merton model\u003c\/li\u003e \u003cli\u003eHedging strategies and transaction costs\u003c\/li\u003e \u003cli\u003eThe behavior of the volatility smile\u003c\/li\u003e \u003cli\u003eStatic and dynamic replication of standard and exotic options\u003c\/li\u003e \u003cli\u003eNew models: their origin, implementation, and consequences\u003c\/li\u003e \u003cli\u003eLocal volatility\u003c\/li\u003e \u003cli\u003eStochastic volatility\u003c\/li\u003e \u003cli\u003eJump-diffusion\u003c\/li\u003e\n\u003c\/ul\u003e ","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47990364504293,"sku":"NP9781118959169","price":90.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118959169.jpg?v=1761787525","url":"https:\/\/k12savings.com\/products\/the-volatility-smile-isbn-9781118959169","provider":"K12savings","version":"1.0","type":"link"}