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• Preface
• Acknowledgments
• About the Authors
• Chapter 1: Overview
• Introduction
• The Black-Scholes-Merton Model and Its Discontents
• A Quick Look at the Implied Volatility Smile
• No-Nonsense Financial Modeling
• The Purpose of Models
• Note
• Chapter 2: The Principle of Replication
• Replication
• Modeling the Risk of Underliers
• The Key Question of Investing
• Derivatives Are Not Independent Securities
• End-of-Chapter Problems
• Notes
• Chapter 3: Static and Dynamic Replication
• Exact Static Replication
• A Simplified Explanation of Dynamic Replication
• End-of-Chapter Problems
• Note
• Chapter 4: Variance Swaps: A Lesson in Replication
• The Volatility Sensitivity of an Option
• Volatility and Variance Swaps
• Replicating Volatility Swaps
• Replicating Variance Swaps out of Options in a Black-Scholes-Merton World
• A Portfolio of Vanilla Options with 1/K2 Weights Produces a Log Payoff
• Proof That the Fair Value of a Log Contract with S* = S0 Is the Realized Future Variance
• The VIX Volatility Index
• End-of-Chapter Problems
• Notes
• Chapter 5: The P&L of Hedged Option Strategies in a Black-Scholes-Merton World
• The Black-Scholes-Merton Equation
• The P&L of Hedged Trading Strategies
• The Effect of Different Hedging Strategies in the BSM World
• End-of-Chapter Problems
• Notes
• Chapter 6: The Effect of Discrete Hedging on P&L
• Replication Errors from Discrete Rebalancing
• An Example
• Conclusion: Accurate Replication and Hedging Are Very Difficult
• End-of-Chapter Problems
• Note
• Chapter 7: The Effect of Transaction Costs on P&L
• The Effect of Transaction Costs
• Analytical Approximation of the Effect of Transaction Costs
• End-of-Chapter Problems
• Note
• Chapter 8: The Smile: Stylized Facts and Their Interpretation
• Smile, Term Structure, Surface, and Skew
• How to Graph the Smile
• Delta and the Smile
• Consequences of the Smile for Trading
• End-of-Chapter Problems
• Notes
• Chapter 9: No-Arbitrage Bounds on the Smile
• No-Arbitrage Bounds on the Smile
• End-of-Chapter Problems
• Notes
• Chapter 10: A Survey of Smile Models
• An Overview of Smile-Consistent Models
• Problems Caused by the Smile
• End-of-Chapter Problem
• Chapter 11: Implied Distributions and Static Replication
• Implied Distributions
• The Breeden-Litzenberger Formula
• Static Replication: Valuing Arbitrary Payoffs at a Fixed Expiration Using Implied Distributions
• The Black-Scholes-Merton Risk-Neutral Probability Density
• End-of-Chapter Problems
• Note
• Chapter 12: Weak Static Replication
• Summary of the Book So Far
• Introducing Weak Static Replication
• Some Insights into the Static Replication of Barrier Options
• Another Approach: Static Replication of an Up-and-Out Call
• End-of-Chapter Problems
• Notes
• Chapter 13: The Binomial Model and Its Extensions
• The Binomial Model for Stock Evolution
• The Binomial Model for Options Valuation
• Extending the Black-Scholes-Merton Model
• End-of-Chapter Problems
• Chapter 14: Local Volatility Models
• Modeling a Stock with Variable Volatility
• Binomial Local Volatility Modeling
• The Relationship between Local Volatility and Implied Volatility
• Difficulties with Binomial Trees
• Further Reading
• End-of-Chapter Problems
• Notes
• Chapter 15: Consequences of Local Volatility Models
• Dupire’s Equation for Local Volatility
• Understanding the Equation
• A Binomial Derivation of the Dupire Equation
• A More Formal Proof of the Dupire Equation
• An Exact Relationship between Local and Implied Volatilities and Its Consequences
• End-of-Chapter Problems
• Chapter 16: Local Volatility Models: Hedge Ratios and Exotic Option Values
• Hedge Ratios in Local Volatility Models
• The Theoretical Value of Exotic Options in Local Volatility Models
• End-of-Chapter Problems
• Notes
• Chapter 17: Some Final Remarks on Local Volatility Models
• The Pros and Cons of Local Volatility Models
• Testing the Local Volatility Model for Index Options
• Note
• Chapter 18: Patterns of Volatility Change
• Heuristic Relationships between the Slope of the Skew and Its Dynamics
• Toward Stochastic Volatility Models
• End-of-Chapter Problems
• Chapter 19: Introducing Stochastic Volatility Models
• Introduction to Stochastic Volatility
• A Heuristic Approach for Introducing Stochastic Volatility into the Black-Scholes-Merton Model
• End-of-Chapter Problems
• Notes
• Chapter 20: Approximate Solutions to Some Stochastic Volatility Models
• Extending the Local Volatility Model
• Extending the BSM Model: Valuing Options with Stochastic Volatility via the Replication Principle
• The Characteristic Solution to the Stochastic Volatility Model
• End-of-Chapter Problem
• Chapter 21: Stochastic Volatility Models: The Smile for Zero Correlation
• The Zero-Correlation Smile Depends on Moneyness
• The Zero Correlation Smile Is Symmetric
• Two-State Stochastic Path Volatility: An Example
• The Smile for GBM Stochastic Volatility with Zero Correlation
• End-of-Chapter Problem
• Note
• Chapter 22: Stochastic Volatility Models: The Smile with Mean Reversion and Correlation
• Mean-Reverting Volatility with Zero Correlation
• Nonzero Correlation in Stochastic Volatility Models
• Comparison of Hedge Ratios under Black-Scholes-Merton, Local Volatility, and Stochastic Volatility
• Best Stock-Only Hedge in a Stochastic Volatility Model
• Concluding Remarks
• Further Reading
• End-of-Chapter Problems
• Notes
• Chapter 23: Jump-Diffusion Models of the Smile: Introduction
• Jumps
• Modeling Pure Jumps
• End-of-Chapter Problems
• Note
• Chapter 24: The Full Jump-Diffusion Model
• Jumps Plus Diffusion
• Trinomial Jump-Diffusion and Calibration
• Valuing a Call in the Jump-Diffusion Model
• A Mixing Formula
• A Qualitative Description of the Jump-Diffusion Smile
• A Simplified Treatment of Jump-Diffusion with a Small Probability of a Large Single Jump
• Further Thoughts and Reading
• End-of-Chapter Problems
• Epilogue
• Appendix A: Some Useful Derivatives of the Black-Scholes-Merton Model
• Appendix B: Backward Itô Integrals
• Standard Integration
• Stochastic Integration
• Note
• Appendix C: Variance Swap Piecewise-Linear Replication
• Answers to End-of-Chapter Problems
• References
• Index
• EULA