Estimating default probabilities for CDO's : a regime switching model

In this paper we estimate default probabilities for synthetic CDO's. These kind of CDO's have a basket of CDS's as underlying portfolio. For pricing purposes and to set tranches for CDO's, default probabilities are important. We adopt the interacting particle system (IPS) approach to compute these kind of rare probabilities. By choosing two different potential functions for the IPS algorithm, we have two approaches. We adopt a structural model with a regime switch in the market volatility for the asset values of the firms. A firm defaults if the asset value falls below a certain threshold D. From the numerical results, we see that the switch in the market volatility and the correlation factor in the underlying portfolio have the biggest impact on the default probabilities in a CDS portfolio.