[eBook Code] Advanced Equity Derivatives (eBook Code, 1st)

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