Preface
Equity hybrid derivatives are a very young class of structures which have drawn a lot of attention over the past two years for many different reasons. Equity hybrid derivatives combine all existing, and therefore established, asset classes like equity, credit, interest rate, foreign exchange, and commodity derivatives. Hence, they present a very interesting challenge to combining different modeling techniques and thereby forming a solid hybrid model framework. This is why we have again decided to publish a book entirely concerned with this very interesting topic. Hybrid derivatives are a strategic and profitable business that every serious top-tier investment bank needs to offer to its client base and are therefore an integral part of its derivatives business.
In this volume, we have not tried to write an introductory text: we have assumed some prior familiarity with mathematics and finance. Part One of this book gives insight into different volatility models (Heston, SABR etc) and their applications to equity markets. It also contains some very recent developments such as variance swap market models. Part Two gives a brief review of short rate models and their incorporation into equity-interest rate hybrid structures. Important examples are discussed, such as the conditional trigger swap (CTS), convertible bonds, and the very popular CPPI structures. Part Three contains a thorough introduction to credit modeling and its importance to equity-credit hybrid derivative structures. Pricing and calibration techniques are also discussed in detail, and important examples like the EDS (equity default swap) are given. Part Four is dedicated to advanced pricing techniques applied to various hybrid and callable structures. We start with copulas applied to equity and credit derivatives (Altiplanos and default baskets), then discuss forward PDEs and local volatility calibration techniques and their application to equity-rate hybrids. This is followed by a thorough presentation of numerical solutions for multi-factor pricing problems, including an important example, the convertible bond. Finally, we conclude with an exposition of American Monte Carlo techniques for derivative pricing.
We would like to offer our special thanks to Professor Alexander Schied for careful reading of the manuscript and valuable comments. We would also like to express our gratitude to Kenji Felgenhauer, Eric Bensoussan, Peter Carr, and Maria Noguieras.
The Authors
London