The Volatility Smile

"The Volatility Smile: An Introduction for Students and Practitioners The Black-Scholes-Merton options 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 EmanuelDerman 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"--

"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"--

The Simplest Rebalancing Strategy: Rebalancing at Regular Intervals.

The Volatility Smile; Contents; Preface; Acknowledgments; About the Authors; 1 Overview; Introduction; The Black-Scholes-Merton Model and Its Discontents; A Quick Look at the Implied Volatility Smile; No-Nonsense Financial Modeling; About Theorems and Laws; On Financial Engineering; The Purpose of Models; A Simple but Prototypical Financial Model; Additional Advantages of Using a Model; Styles of Modeling: What Works and What Doesn't; 2 The Principle of Replication; Replication; The One Law of Quantitative Finance; Valuation by Replication; Styles of Replication; The Limits of Replication.

Modeling the Risk of UnderliersThe Efficient Market Hypothesis; Uncertainty, Risk, and Return; The Behavior of a Share of Stock; The Risk of Stocks; Riskless Bonds; The Key Question of Investing; Some Investment Risks Can Be Avoided; World #1: Only a Few Uncorrelated Stocks and a Riskless Bond; World #2: An Infinite Number of Uncorrelated Stocks and a Riskless Bond; World #3: An Infinite Number of Stocks All Simultaneously Correlated with the Entire Market, and a Riskless Bond; Derivatives Are Not Independent Securities; End-of-Chapter Problems; 3 Static and Dynamic Replication.

Exact Static R…