Copulas are
currently one of the hot topics in quantitative finance. In a nutshell, copulas
are a generalization of correlation. Suppose you have marginal distributions for
the components of a random vector. With copulas, you can fill in the
interdependencies between those components to obtain the joint distribution of
the random vector. Depending on what copula you use, you can achieve different
interdependencies. Copulas are transforming aspects of financial engineering,
portfolio credit risk measurement and value-at-risk.
For professionals
with strong quantitative skills and a firm background in financial engineering,
this is an accessible but in-depth introduction to copulas. Be forewarned that
the authors introduce copulas in the context of financial engineering examples.
If you know financial engineering, that discussion is enlightening. If you don't
know financial engineering (perhaps you are only interested in using copulas in
portfolio credit risk measurement or value-at-risk) you will be lost.
Contents
1. Derivatives
pricing, hedging and risk management
2. Bivariate
copula functions
3. Market
comovements and copula families
4. Multivariate
copulas
5. Estimation and
calibration from market data
6. Simulation of
market scenarios
7. Credit risk
applications
8. Option pricing
with copulas
The book opens
with a review of important topics in financial engineering. It then introduces
copulas in the context of pricing exotic derivatives. Chapters 2 through 4
are largely mathematical, describing the mathematics of bivariate and
multivariate copulas. Concepts are, however, illustrated with financial
applications, such as value-at-risk. Chapter 5 describes how to estimate and
calibrate copulas from market data. Chapter 6 explains how to generate random
variates for Monte Carlo simulations when joint distributions are specified with
copulas. Ease of use in Monte Carlo analyses is one of the strengths of copulas.
Chapters 7 and 8 close with applications to CDO portfolio credit risk modeling and
options pricing.
Overall, this is
an exceptional book. For sophisticated readers, it is accessible, theoretically
precise and eminently practical. I have only two caveats: 1) you will need a
fairly strong background in financial engineering, and 2) applications to
value-at-risk are mentioned only briefly. If you are interested in mastering
copulas for use in financial engineering or portfolio credit risk measurement, I can't recommend the book
highly enough. Read it side-by-side with Nelsen (1999).
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