Credit Risk Premia and Quadratic BSDEs with a Single Jump

by Stefan Ankirchner of the Universtät Bonn,
Christophette Blanchet-Scalliet of the Université de Lyon, and
Anne Eyraud-Loisel of the Université Lyon 1

June 8, 2010

Abstract: This paper is concerned with the determination of credit risk premia of defaultable contingent claims by means of indifference valuation principles. Assuming exponential utility preferences we derive representations of indifference premia of credit risk in terms of solutions of Backward Stochastic Differential Equations (BSDE). The class of BSDEs needed for that representation allows for quadratic growth generators and jumps at random times. Since the existence and uniqueness theory for this class of BSDEs has not yet been developed to the required generality, the first part of the paper is devoted to fill that gap. By using a simple constructive algorithm, and known results on continuous quadratic BSDEs, we provide sufficient conditions for the existence and uniqueness of quadratic BSDEs with discontinuities at random times.

JEL Classification: C61, C11.

AMS Classification: 60H10, 60J75, 91B28, 91B70, 93E20.

Published in: International Journal of Theoretical and Applied Finance, Vol. 13, No. 7, (November 2010), pp. 1103-1129.

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