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Pricing Credit Derivatives with Uncertain Default Probabilities

by Vivien Brunel of HSBC CCF

January 10, 2001

Abstract: One main problem of credit models, as in stochastic volatility models for instance, is that the range of arbitrage prices of risky bonds and credit derivatives is very wide. In this article, we present a model for pricing options on the spread in an environment where the rating transition probabilities are uncertain parameters. The transition intensities are assumed to lie between two bounds which can be easily interpreted in the light of the rating agencies' transition matrices. These bounds are some kind of confidence interval of the future values of the rating transition intensities. We show that the external arbitrage prices are solutions of a Black-Scholes-Barenblatt equation. In particular, when using realistic values for the rating transition (default) probabilities, the arbitrage range of credit derivatives prices is narrow.

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