Foreword xi
Preface xiii
Acknowledgments xv
Chapter 1 Exotic Derivatives 1
1-1 Single-Asset Exotics 1
1-2 Multi-Asset Exotics 4
1-3 Structured Products 9
References 11
Problems 11
Chapter 2 The Implied Volatility Surface 15
2-1 The Implied Volatility Smile and Its Consequences 15
2-2 Interpolation and Extrapolation 20
2-3 Implied Volatility Surface Properties 22
2-4 Implied Volatility Surface Models 22
References 29
Problems 30
Chapter 3 Implied Distributions 33
3-1 Butterfly Spreads and the Implied Distribution 33
3-2 European Payoff Pricing and Replication 36
3-3 Pricing Methods for European Payoffs 39
3-4 Greeks 41
References 42
Problems 42
Chapter 4 Local Volatility and Beyond 45
4-1 Local Volatility Trees 45
4-2 Local Volatility in Continuous Time 46
4-3 Calculating Local Volatilities 48
4-4 Stochastic Volatility 50
References 55
Problems 55
Chapter 5 Volatility Derivatives 59
5-1 Volatility Trading 59
5-2 Variance Swaps 61
5-3 Realized Volatility Derivatives 65
5-4 Implied Volatility Derivatives 67
References 70
Problems 70
Chapter 6 Introducing Correlation 73
6-1 Measuring Correlation 73
6-2 Correlation Matrices 75
6-3 Correlation Average 77
6-4 Black-Scholes with Constant Correlation 82
6-5 Local Volatility with Constant Correlation 84
References 84
Problems 85
Chapter 7 Correlation Trading 87
7-1 Dispersion Trading 87
7-2 Correlation Swaps 91
Problems 93
Chapter 8 Local Correlation 95
8-1 The Implied Correlation Smile and Its Consequences 95
8-2 Local Volatility with Local Correlation 97
8-3 Dynamic Local Correlation Models 99
8-4 Limitations 99
References 100
Problems 100
Chapter 9 Stochastic Correlation 103
9-1 Stochastic Single Correlation 103
9-2 Stochastic Average Correlation 104
9-3 Stochastic Correlation Matrix 108
References 111
Problems 111
Appendix A Probability Review 115
A-1 Standard Probability Theory 115
A-2 Random Variables, Distribution, and Independence 116
A-3 Conditioning 117
A-4 Random Processes and Stochastic Calculus 118
Appendix B Linear Algebra Review 119
B-1 Euclidean Spaces 119
B-2 Square Matrix Decompositions 120
Solutions Manual 123
Author's Note 143
About the Author 145
Index 147
