Correlated defaults – the portfolio approach

In this section, we show you how to deal with correlated random variables with copulas for the simulation of loss distributions of credit portfolios. The copula function is a joint cumulative distribution function of uniform distributed random variables. The copula function contains all the information on the dependence structure of the components. Any of the continuously distributed random variables can be transformed into uniformly distributed variables, which allows for the possibility of general modeling; for example, it can be combined with the structural approach. Using the copula package, we demonstrate how to simulate two uniformly distributed random variables with Gaussian and t-copulas, and how to fit in a Gaussian copula parameter from the generated data. (One can apply this method for historical datasets also.) This package also serves useful functions in a wide range of topics about copulas, such as plotting or fitting copula classes...