Copula Methods in Finance

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收藏 2007-09-19

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 2004 版
Outline of the book Chapter 1 reviews the state of the art in asset pricing and risk management, going over the major frontier issues and providing justifications for introducing copula functions. Chapter 2 introduces the reader to the bivariate copula case. It presents the mathematical and probabilistic background on which the applications are built and gives some first examples in finance. Chapter 3 discusses the flaws of linear correlation and highlights how copula functions, along with non-parametric association measures, may provide a much more flexible way to represent market comovements. Chapter 4 extends the technical tools to a multivariate setting. Readers who are not already familiar with copulas are advised to skip this chapter at first reading (or to read it at their own risk!). Chapter 5 explains the statistical inference for copulas. It covers both methodological aspects and applications from market data, such as calibration of actual risk factors comovements and VaR measurement. Here the readers can find details on the classical estimation methods as well as on most recent approaches, such as the conditional copula. Chapter 6 is devoted to an exhaustive account of simulation algorithms for a large class of multivariate copulas. It is enhanced by financial examples. Chapter 7 presents credit risk applications, besides giving a brief introduction to credit derivative markets and instruments. It applies copulas to the pricing of complex credit structures such as basket default swaps and CDOs. It is shown how to calibrate the pricing Preface xiii model to market data. Its sensitivity with respect to the copula choice is accounted for in concrete examples. Chapter 8 covers option pricing applications. Starting from the bivariate pricing kernel, copulas are used to evaluate counterparty risk in derivative transactions and bivariate rainbow options, such as options to exchange. We also show how the barrier option pricing problem can be cast in a bivariate setting and can be represented in terms of copulas. Finally, the estimation and simulation techniques presented in Chapters 5 and 6 are put at work to solve the evaluation problem of a multivariate basket option.