Copulas provide us with a tool for constructing multivariate distributions with arbitrary marginal distributions and a wide range of dependence structures. The aim of this book is to describe what the practitioner, or scientist, needs to know about copulas. Although the emphasis is on financial applications, the general theory is relevant for any multivariate setting. The outline of the book is as follows. Chapter 2 is a discussion of multivariate distribution functions that are useful for financial data. In chapter 3 we proceed with a discussion of commonly used dependence measures, and we highlight deficiencies of the correlation coefficient. We start chapter 4 by describing the properties a general function must satisfy in order to be a copula, and goes on by describing the properties of the most common copulas. In chapter 5 we discuss the problem of estimating the parameters in a copula, and in chapter 6 we review the recent goodness-of-fit procedures suggested in the literature. Chapter 7 is a short review of some of the main applications of copulas in relation to credit risk models.

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