Pricing CDO tranches in an intensity based model with the mean reversion approach

We discuss the phenomenon of mean reversion in credit risk market and propose a class of models, in the framework of intensity based model, where the default intensity is composed of a common component and a idiosyncratic component which are specified by independent mean reverting stochastic processes of the following Markovian type dX (t) = (theta + sigma alpha (X(t), t))X(t)dt + sigma X(t)dW(t) where theta >= 0 the long-term mean value, the parameter sigma >= 0 stands for the scaling of the volatility, and alpha(X(t), t)is the mean correction with the function alpha : R x [0, infinity) bar right arrow alpha(x,t) is an element of R being twice differentiable in x and differentiable in t, and W (t) is a Brownian motion. We demonstrate how this class of models can be used to price synthetic CDOs and present a closed-form solution of tranche spreads in synthetic CDOs. (C) 2010 Elsevier Ltd. All rights reserved.