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

Wu, JiangLun and Yang, Wei (2010) Pricing CDO tranches in an intensity based model with the mean reversion approach. Mathematical and Computer Modelling, 52 (5-6). pp. 814-825. ISSN 0895-7177

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Abstract

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 where θ≥0 is the long-term mean value, the parameter σ≥0 stands for the scaling of the volatility, and α(X(t),t) is the mean correction with the function α:R×[0,∞)↦α(x,t)∈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.