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Utility valuation of multi-name credit derivatives and application to CDOs

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  • Ronnie Sircar
  • Thaleia Zariphopoulou

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.

Suggested Citation

  • Ronnie Sircar & Thaleia Zariphopoulou, 2010. "Utility valuation of multi-name credit derivatives and application to CDOs," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 195-208.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:2:p:195-208
    DOI: 10.1080/14697680902744737
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    Citations

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    Cited by:

    1. Jinbeom Kim & Tim Leung, 2016. "Impact of risk aversion and belief heterogeneity on trading of defaultable claims," Annals of Operations Research, Springer, vol. 243(1), pages 117-146, August.
    2. Ying Jiao & Huyên Pham, 2011. "Optimal investment with counterparty risk: a default-density model approach," Finance and Stochastics, Springer, vol. 15(4), pages 725-753, December.
    3. Shican Liu & Yanli Zhou & Benchawan Wiwatanapataphee & Yonghong Wu & Xiangyu Ge, 2018. "The Study of Utility Valuation of Single-Name Credit Derivatives with the Fast-Scale Stochastic Volatility Correction," Sustainability, MDPI, vol. 10(4), pages 1-21, March.
    4. John R. Birge & Lijun Bo & Agostino Capponi, 2018. "Risk-Sensitive Asset Management and Cascading Defaults," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 1-28, February.
    5. Vicky Henderson & Gechun Liang, 2011. "A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk," Papers 1111.3856, arXiv.org, revised Sep 2015.
    6. Konstantinos Spiliopoulos, 2014. "Systemic Risk and Default Clustering for Large Financial Systems," Papers 1402.5352, arXiv.org, revised Feb 2015.

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