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

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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 (https://doi.org/10.1016/j.mcm.2010.05.012)

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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.

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