SÉBASTIEN BOSSU is Principal at Ogee Group LLC, an investment management and software development business based in New York. His past experience includes positions as director of Equity Derivatives Structuring for a London bank and exotics structurer at J.P. Morgan. Bossu is currently an adjunct professor at Pace University and also recently taught at Fordham University.

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