Advanced Equity Derivatives: Volatility and Correlation

ISBN-13: 9781118750964 / Angielski / Twarda / 2014 / 176 str.

Sebastien Bossu

Opis

In Advanced Equity Derivatives: Volatility and Correlation, Sebastien 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.

Spis treści

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

O autorze

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.

Blurb

Praise for Advanced Equity Derivatives

"Written by a leading expert who spearheaded the joint pricing and modeling of equity volatility and correlation swaps, this book covers all the theory, models, and practical issues essential for everyone on the buy– or sell–side involved in the pricing and risk management of options. A superb read and a must–read for graduate students studying the subject."
Martin Bertsch, Co–Founder of Kledia Consulting and MyFinanceTutor

"A great resource for academics, practitioners, and graduate students. Sébastien Bossu is the definite expert on how to link volatility and correlation together."
François Brochet, Harvard Business School

"Sébastien Bossu shares his knowledge of sophisticated derivatives concepts, instruments and strategies used by traders, investment managers, and risk managers. Understanding volatility and correlation in depth is crucial to successfully pricing and hedging equity options. This book is a must–have in this highly specialized field."
Kay Torshen, CEO and Founder, Torshen Capital Management LLC

Accurate pricing strategies for cutting–edge exotic derivatives

For equity derivative traders and quantitative analysts who need to understand the latest models in pricing and hedging advanced equity instruments, this book is the perfect choice. Sébastien Bossu gets down to details immediately, concisely presenting single– and multi–asset exotics before moving into the key concepts that sophisticated traders need to know. Advanced Equity Derivatives addresses everything from well–established volatility instruments to the most advanced correlation models.

With Advanced Equity Derivatives, readers gain a highly developed understanding of complex issues related to volatility and correlation, including:

• Implied volatility surface models and their consequence for the pricing of exotics
• Pricing European payoffs using implied distributions
• Local and stochastic volatility models
• Variance swaps and other volatility derivatives
• Extending Black–Scholes and local volatility models to include correlation assets
• Dispersion trading and correlation swaps
• Local and stochastic correlation models and matrices