In Advanced Equity Derivatives: Volatility and Correlation, Sébastien Bossu reviews and explains the advanced concepts used for pricing and hedging equity exotic derivatives. Designed for financial modelers, option traders and sophisticated investors, the content covers the most important theoretical and practical extensions of the Black-Scholes model.
Each chapter includes numerous illustrations and a short selection of problems, covering key topics such as implied volatility surface models, pricing with implied distributions, local volatility models, volatility derivatives, correlation measures, correlation trading, local correlation models and stochastic correlation.
The author has a dual professional and academic background, making Advanced Equity Derivatives: Volatility and Correlation the perfect reference for quantitative researchers and mathematically savvy finance professionals looking to acquire an in-depth understanding of equity exotic derivatives pricing and hedging.
Table of Contents
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
