Advanced Equity DerivativesVolatility and Correlation
Wiley Finance 1. Aufl.
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.
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
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.
Equity exotic derivatives are staples of sophisticated investment and portfolio management strategies. Knowing the formulas that lead to correct fair value pricing and hedging of these instruments is requisite for trading equity-linked products and enhancing yields. Advanced Equity Derivatives is a resource for traders, analysts, and other finance professionals who want to gain an in-depth understanding of how these advanced instruments work. This book ventures far beyond vanilla products and instruments that were considered exotic thirty years ago, making it a definitive text in the field. Written for readers with a solid background in basic equity derivatives pricing and advanced mathematics, this book references Black-Scholes and other standard formulas for exotics from the most common to the cutting-edge. With this background, readers can make use of detailed discussions of central concepts in advanced equity derivatives. Implied distributions, volatility derivatives, and correlation trading are among the topics addressed, and each chapter concludes with practice exercises and important derivations. Numerous illustrations allow readers to quickly grasp complicated concepts. Sébastien Bossu is a highly experienced exotics specialist. In Advanced Equity Derivatives, he presents his own work alongside the work of others in the field in order to prepare readers to accurately price next-generation instruments. In 2004, Bossu discovered a model that corrected errors in the pricing and hedging of correlation swaps, and this model forms the basis for the correlation chapters of this book. Other possibilities, including stochastic correlation models, are also thoroughly explored, giving readers a sufficient understanding to transpose formulas into any context. This book builds on the concepts and principles explained by Bossu's popular textbook, An Introduction to Equity Derivatives. For investment professionals who need to go beyond the basics to manage risk and understand pricing models, this book is the indispensable next step. The front line of current equity exotics research is repre??sented in the pages of Advanced Equity Derivatives. From standard instruments to brand new practices, this text quickly brings readers up to date on Wall Street standards and the direction of equity exotic derivatives markets.
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
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