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The Volatility Smile
The 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.
The Volatility Smile 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.
Topics covered include:
- The principles of valuation
- Static and dynamic replication
- The Black-Scholes-Merton model
- Hedging strategies
- Transaction costs
- The behavior of the volatility smile
- Implied distributions
- Local volatility models
- Stochastic volatility models
- Jump-diffusion models
- Sales Rank: #102100 in Books
- Published on: 2016-09-06
- Original language: English
- Number of items: 1
- Dimensions: 9.84" h x .59" w x 5.91" l, .0 pounds
- Binding: Hardcover
- 528 pages
From the Inside Flap
The Volatility Smile provides an access- ible 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, The Volatility Smile 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, The Volatility Smile is also a book about how to evaluate and build financial models.
Prior 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.
Good 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.
From the Back Cover
The Black-Scholes-Merton option model was the greatest innovation of twentieth century finance, 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.
Option 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, The Volatility Smile 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:
- The principles of valuation
- The Black-Scholes-Merton model
- Hedging strategies and transaction costs
- The behavior of the volatility smile
- Static and dynamic replication of standard and exotic options
- New models: their origin, implementation, and consequences
- Local volatility
- Stochastic volatility
- Jump-diffusion
About the Author
EMANUEL DERMAN is a professor at Columbia University, where he directs its financial engineering program. He is the author of My Life as a Quant and Models.Behaving.Badly.
MICHAEL B. MILLER is the founder and CEO of Northstar Risk Corp. He is the author of Mathematics and Statistics for Financial Risk Management, Second Edition.
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