Utility Valuation of Multiname Credit Derivatives and Application to CDOs

by Ronnie Sircar of Princeton University, and
Thaleia Zariphopoulou of the University of Texas at Austin

July 2008

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 analyze resulting yield spreads in multiname 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 analyze 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.

Keywords: Credit derivatives, indifference pricing.

Published in: Quantitative Finance, Vol. 10, No. 2, (February 2010), pp. 195-208.

Previously titled: Utility Valuation of Credit Derivatives and Application to CDOs

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