Modeling the Term Structure of Defaultable Bonds under Recovery Risk
by Lotfi Karoui of McGill University
November 17, 2005
Abstract: Although the Basle Committee has identified recovery risk as an important source of risk in addition to default, the impact of recovery rates on bond prices is not yet fully understood in the literature. This paper proposes a reduced form discrete-time approach for pricing defaultable securities incorporating stochastic recovery rates. We provide pricing formulas for risky bonds and CDS contracts in the case of an economy with an affine state vector. We show that our methodology provides a tractability that is usually typical of continuous time models. The model stays tractable even in the case of rich and realistic econometric representations of the state variables and can therefore be estimated using standard techniques. As an illustration, several specifications for the state variables are discussed and a numerical example is provided.
Keywords: defaultable bonds, CDS contracts, correlation, stochastic recovery rates, discrete time.