Credit Derivatives: Trading, Investing and Risk Management, Second Edition

23

Alternative Copulas

We look at other Copulas for three main reasons:

1. Producing correlated default times based on Student’s t-distribution is commonly talked about in the literature and often used in practice.

2. Having an alternative Copula is a worthwhile model test and risk-control measure.

3. Some other Copulas - in particular Clayton and the ‘Archimedean’ class of Copulas - give a different perspective on the Normal Copula and its application, and are also discussed frequently in the literature.

Student’s t-distribution is a simple extension of the Normal case, and some useful results that require relatively little effort are contained in this chapter. Sections 23.2 to 23.4 are more specialised, but the general reader is recommended to read the ‘implications’ at the end of section 23.3 at least.

23.1 STUDENT’S t-DISTRIBUTION

Student’s t-distribution is similar to the Normal when the ‘degrees of freedom’ are large. It is a simple extension of the Normal model in terms of implementation, and is widely discussed in the literature as an alternative - and an improvement - on the Normal Copula.

 

Random numbers from Student’s t-distribution with d degrees of freedom

1. Generate N correlated random numbers, x, from the Normal distribution as already described, and d independent Normal random numbers X_j.

2. Calculate an independent (which is from the Chi-squared distribution ...