CDO pricing using archimedean copula with dynamic structure

This paper considers the problem of CDO pricing with dynamic Archimedean copula. The classical Archimedean copula is extended to the case with dynamic structure by introducing two continuous stochastic processes to describe both the systematic factor and idiosyncratic factors, which is needed when price CDO options or forward starting CDOs. We focus on Clayton copula which is a special kind of Archimedean copula with lower tail dependence. Then we convert the two stochastic processes to fit the distribution implied by Clayton copula. For large portfolios, loss distribution can be directly got from default probability which is quoted from CDS market. For the general case, characteristic function of the accumulated loss can be derived and using the fast Fourier transform, loss distribution can also be calculated. Numerical results are presented at the end.