## 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.

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.

Original language | English |
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Pages (from-to) | 814-825 |

Number of pages | 12 |

Journal | Mathematical and Computer Modelling |

Volume | 52 |

Issue number | 5-6 |

DOIs | |

Publication status | Published - Sep 2010 |

## Keywords

- credit risk
- intensity based model
- mean reversion
- collateralized debt obligations (CDOs)
- cashflow CDO
- synthetic CDO