Pricing portfolio credit derivatives with stochastic recovery and systematic factor

In this paper, a model for pricing portfolio credit derivatives with nested Archimedean copulas, stochastic recovery rates, and an exogenous systematic factor is presented. The model explains the dependence between default probabilities and recovery rates, both of which are affected by risk of changing in portfolio value because of modifications of a systematic factor. We call this risk "economic change risk ". The advantage of the model is that the systematic factor is able to be set optimally. This leads that when we compute prices, we can consider the economic state directly using the proposed model. The paper demonstrates pricing basket credit default swaps (basket CDSs) as an example of portfolio credit derivatives. The effects of basket CDS prices and the dependence structures from the change in economic change risk through numerical experiments are investigated. The results of the experiments show that the model with economic change risk evaluates higher spreads and stronger dependence than those in the existing researches. Moreover, the effects of economic change risk differ according to the choice of copulas and recovery rates.