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Modeling Defaultable Securities with Recovery Risk

by Lotfi Karoui of McGill University

January 2007

Abstract: Although the Basel Committee has identified recovery risk as an important source of risk in relation to default, the impact of recovery rates on defaultable securities is not yet well understood. This paper proposes a discrete-time reduced form approach for pricing defaultable securities that incorporates stochastic recovery rates. We provide pricing formulas for risky bonds and credit default swap contracts in the case of an economy with an affine state vector. Faced with rich and realistic econometric representations of the state variables, the model stays tractable and can be estimated using standard techniques. We estimate a five-factor Gaussian model on BBB and B Standard & Poor's yield indices. Our analysis indicates that for both indices, the stochastic recovery model significantly outperforms a nested model where the unconditional recovery rate is estimated as a constant. The model is able to capture two important stylized facts of defaultable securities: The positive correlation between the loss given default, and the intensity of default and the negative correlation between the intensity of default and the risk-free interest rate.

JEL Classification: G12, G13.

Keywords: defaultable bonds, credit default swap contracts, stochastic recovery rate, discrete time.

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