### Abstract

We study the impact of risk-aversion on the valuation of credit derivatives. Using the technology of utility-indifference pricing in intensity-based models of default risk, we analyse resulting yield spreads in multi-name credit derivatives, particularly CDOs. We study first the idealized problem with constant intensities where solutions are essentially explicit. We also give the large portfolio asymptotics for this problem. We then analyse the case where the firms have stochastic default intensities driven by a common factor, which can be viewed as another extreme from the independent case. This involves the numerical solution of a system of reaction-diffusion PDEs. We observe that the nonlinearity of the utility-indifference valuation mechanism enhances the effective correlation between the times of the credit events of the various firms leading to non-trivial senior tranche spreads, as often seen from market data.

Original language | English (US) |
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Pages (from-to) | 195-208 |

Number of pages | 14 |

Journal | Quantitative Finance |

Volume | 10 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2010 |

### All Science Journal Classification (ASJC) codes

- Finance
- Economics, Econometrics and Finance(all)

### Keywords

- Applications to credit risk
- Applications to default risk
- Applied mathematical finance
- Continuous time finance
- Control of stochastic systems
- Pricing of derivatives securities
- Pricing with utility based preferences
- Utility indifference

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## Cite this

*Quantitative Finance*,

*10*(2), 195-208. https://doi.org/10.1080/14697680902744737