The volatility smile : an introduction for students and practitioners

Intro -- 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 Underliers -- The 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 Replication -- Put-Call Parity -- Replicating a Collar -- Generalized Payoffs -- Approximate Static Hedge for a European Down-and-Out Call -- A Simplified Explanation of Dynamic Replication -- What Should You Pay for Convexity? -- The Distinction between Implied Volatility and Realized Volatility -- Notation for Implied Variables -- Hedging an Option Means Betting on Volatility -- End-of-Chapter Problems -- 4 Variance Swaps -- The Volatility Sensitivity of an Option -- Volatility and Variance Swaps -- Replicating Volatility Swaps.