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A general framework for pricing credit risk. (English) Zbl 1134.91395
Summary: A framework is provided for pricing derivatives on defaultable bonds and other credit-risky contingent claims. The framework is in the spirit of reduced-form models, but extends these models to include the case that default can occur only at specific times, such as coupon payment dates. Although the framework does not provide an efficient setting for obtaining results about structural models, it is sufficiently general to include most structural models, and thereby highlights the commonality between reduced-form and structural models. Within the general framework, multiple recovery conventions for contingent claims are considered: recovery of a fraction of par, recovery of a fraction of a no-default version of the same claim, and recovery of a fraction of the pre-default value of the claim. A stochastic-integral representation for credit-risky contingent claims is provided, and the integrand for the credit exposure part of this representation is identified. In the case of intensity-based, reduced-form models, credit spread and credit-risky term structure are studied.
MSC:
91B28Finance etc. (MSC2000)
60H05Stochastic integrals
60H30Applications of stochastic analysis