A mixed PDE-Monte Carlo approach for pricing credit default index swaptions

The problem of numerically pricing credit default index swaptions on a large number of names is considered. We place ourselves in a stochastic intensity framework, where Ornstein-Uhlenbeck-type correlated processes are used to model both firms' distance to default and a macroeconomic state variable. Here the default of the firms' follows the reduced-form approach and the (random) intensity of the default depends on the behavior of the diffusion processes. We propose here a numerical method based on both a Monte Carlo and a deterministic approach for solving PDEs by finite differences. Numerical tests demonstrate the efficiency and the robustness of the proposed procedure. © Springer-Verlag 2006.