Cover -- Title Page -- Copyright -- Contents -- Foreword -- Preface -- Acknowledgments -- Chapter 1 Exotic Derivatives -- 1-1 Single-Asset Exotics -- 1-1.1 Digital Options -- 1-1.2 Asian Options -- 1-1.3 Barrier Options -- 1-1.4 Lookback Options -- 1-1.5 Forward Start Options -- 1-1.6 Cliquet Options -- 1-2 Multi-Asset Exotics -- 1-2.1 Spread Options -- 1-2.2 Basket Options -- 1-2.3 Worst-Of and Best-Of Options -- 1-2.4 Quanto Options -- 1-3 Structured Products -- References -- Problems -- 1.1 "Free" Option -- 1.2 Autocallable -- 1.3 Geometric Asian Option -- 1.4 Change of Measure -- 1.5 At-the-Money Lookback Options -- 1.6 Siegel's Paradox -- Appendix 1.A: Change of Measure and Girsanov's Theorem -- Chapter 2 The Implied Volatility Surface -- 2-1 The Implied Volatility Smile and Its Consequences -- 2-1.1 Consequence for the Pricing of Call and Put Spreads -- 2-1.2 Consequence for Hedge Ratios -- 2-1.3 Consequence for the Pricing of Exotics -- 2-2 Interpolation and Extrapolation -- 2-3 Implied Volatility Surface Properties -- 2-4 Implied Volatility Surface Models -- 2-4.1 A Parametric Model of Implied Volatility: The SVI Model -- 2-4.2 Indirect Models of Implied Volatility -- References -- Problems -- 2.1 No Call or Put Spread Arbitrage Condition -- 2.2 No Butterfly Spread Arbitrage Condition -- 2.3 Sticky True Delta Rule -- 2.4 SVI Fit -- Chapter 3 Implied Distributions -- 3-1 Butterfly Spreads and the Implied Distribution -- 3-2 European Payoff Pricing and Replication -- 3-3 Pricing Methods for European Payoffs -- 3-4 Greeks -- References -- Problems -- 3.1 Overhedging Concave Payoffs -- 3.2 Perfect Hedging with Puts and Calls -- 3.3 Implied Distribution and Exotic Pricing -- 3.4 Conditional Pricing -- 3.5 Path-Dependent Payoff -- 3.6 Delta -- Chapter 4 Local Volatility and Beyond -- 4-1 Local Volatility Trees.

4-2 Local Volatility in Continuous Time -- 4-3 Calculating Local Volatilities -- 4-3.1 Dupire's Equation -- 4-3.2 From Implied Volatility to Local Volatility -- 4-3.3 Hedging with Local Volatility -- 4-4 Stochastic Volatility -- 4-4.1 Hedging Theory -- 4-4.2 Connection with Local Volatility -- 4-4.3 Monte Carlo Method -- 4-4.4 Pricing and Hedging Forward Start Options -- 4-4.5 A Word on Stochastic Volatility Models with Jumps -- References -- Problems -- 4.1 From Implied to Local Volatility -- 4.2 Market Price of Volatility Risk -- 4.3 Local Volatility Pricing -- Appendix 4.A: Derivation of Dupire's Equation -- Chapter 5 Volatility Derivatives -- 5-1 Volatility Trading -- 5-2 Variance Swaps -- 5-2.1 Variance Swap Payoff -- 5-2.2 Variance Swap Market -- 5-2.3 Variance Swap Hedging and Pricing -- 5-2.4 Forward Variance -- 5-3 Realized Volatility Derivatives -- 5-4 Implied Volatility Derivatives -- 5-4.1 VIX Futures -- 5-4.2 VIX Options -- References -- Problems -- 5.1 Delta-Hedging P&L Simulation -- 5.2 Volatility Trading with Options -- 5.3 Fair Variance Swap Strike -- 5.4 Generalized Variance Swaps -- 5.5 Call on Realized Variance -- Chapter 6 Introducing Correlation -- 6-1 Measuring Correlation -- 6-1.1 Historical Correlation -- 6-1.2 Implied Correlation -- 6-2 Correlation Matrices -- 6-3 Correlation Average -- 6-3.1 Correlation Proxy -- 6-3.2 Some Properties of the Correlation Proxy -- 6-4 Black-Scholes with Constant Correlation -- 6-5 Local Volatility with Constant Correlation -- References -- Problems -- 6.1 Lower Bound for Average Correlation -- 6.2 Geometric Basket Call -- 6.3 Worst-Of Put Pricing -- 6.4 Continuously Monitored Correlation -- Chapter 7 Correlation Trading -- 7-1 Dispersion Trading -- 7-1.1 Vanilla Dispersion Trades -- 7-1.2 Variance Dispersion Trades -- 7-2 Correlation Swaps -- 7-2.1 Payoff -- 7-2.2 Pricing -- 7-2.3 Hedging.

Problems -- 7.1 -- 7.2 -- 7.3 -- 7.4 -- Chapter 8 Local Correlation -- 8-1 The Implied Correlation Smile and Its Consequences -- 8-2 Local Volatility with Local Correlation -- 8-3 Dynamic Local Correlation Models -- 8-4 Limitations -- References -- Problems -- 8.1 Implied Correlation -- 8.2 Dynamic Local Correlation I -- 8.3 Dynamic Local Correlation II -- Chapter 9 Stochastic Correlation -- 9-1 Stochastic Single Correlation -- 9-2 Stochastic Average Correlation -- 9-2.1 Tradable Average Correlation -- 9-2.2 The B-O Model -- 9-3 Stochastic Correlation Matrix -- 9-3.1 Spectral Decomposition and the Common Factor Model -- 9-3.2 The n × n Fischer-Wright Model -- References -- Problems -- 9.1 -- 9.2 -- Appendix 9.A: Sufficient Condition for Lower Bound Unattainability -- Appendix 9.B: Necessary Condition for Upper Bound Unattainability -- Appendix A Probability Review -- A-1 Standard Probability Theory -- A-1.1 Probability Space -- A-1.2 Filtered Probability Space -- A-1.3 Independence -- A-2 Random Variables, Distribution, and Independence -- A-2.1 Random Variables -- A-2.2 Joint Distribution and Independence -- A-3 Conditioning -- A-4 Random Processes and Stochastic Calculus -- Appendix B Linear Algebra Review -- B-1 Euclidean Spaces -- B-1.1 Inner Product and the Norm -- B-1.2 Cauchy-Schwarz Inequality and Angles -- B-1.3 Orthogonality -- B-2 Square Matrix Decompositions -- Solutions Manual -- Author's Note -- About the Author -- Index.