Pricing collateralized debt obligations with Markov-modulated Poisson processes

Abstract

For the valuation of a CDO (collateralized debt obligation), a standard approach in practice is to employ the Gaussian copula model of (Li, 7) [J. Fixed Income, 2000, 9, 43–54]. However, this model is limited in that its framework is completely static, failing to capture the dynamic evolution of the CDO. In general, portfolio credit derivatives are subject to two kinds of risk, a default event risk, when any underlying firm involved in the CDO fails to fulfill its obligations, and credit spread risk, due to the change of the default intensity over time. In dealing with either type of risk, it is absolutely necessary to develop a dynamic model incorporating the stochastic behavior of the macro-economic conditions and their influence on the default intensity. In this paper, a dynamic stochastic model is developed where the macro-economic conditions are assumed to follow a birth–death process, which would affect loss distributions characterized by a Markov-modulated Poisson process (MMPP). By exploiting the stochastic structure of the MMPP, efficient computational procedures are established for evaluating time-dependent loss distributions and prices of the CDO. Numerical results are presented, demonstrating the potential usefulness of the model by estimating the underlying parameters based on real market data.

Keywords:

• Credit risk
• Credit derivatives
• Markov processes
• Dynamic models