### Abstract

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 |

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### Keywords

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

### Cite this

*Mathematical and Computer Modelling*,

*52*(5-6), 814-825. https://doi.org/10.1016/j.mcm.2010.05.012

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*Mathematical and Computer Modelling*, vol. 52, no. 5-6, pp. 814-825. https://doi.org/10.1016/j.mcm.2010.05.012

**Pricing CDO tranches in an intensity based model with the mean reversion approach.** / Wu, JiangLun; Yang, Wei.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Pricing CDO tranches in an intensity based model with the mean reversion approach

AU - Wu, JiangLun

AU - Yang, Wei

PY - 2010/9

Y1 - 2010/9

N2 - 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 typewhere 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.

AB - 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 typewhere 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.

KW - credit risk

KW - intensity based model

KW - mean reversion

KW - collateralized debt obligations (CDOs)

KW - cashflow CDO

KW - synthetic CDO

U2 - 10.1016/j.mcm.2010.05.012

DO - 10.1016/j.mcm.2010.05.012

M3 - Article

VL - 52

SP - 814

EP - 825

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

SN - 0895-7177

IS - 5-6

ER -