A Modified Reduced-Form Model with Time-Varying Default and Recovery Rates and Its Applications in Pricing Convertible Bonds

Abstract

Due to the lack of proper credit derivatives and opaque financial status of a reference entity, it is difficult to accurately estimate recovery rates in reducedform models. In addition, most reduced-form models adopt a constant recovery rate assumption that fails to capture the time-varying dynamics and inverse relationships between recovery and default rates found in empirical studies. Most revisions that incorporate this inverse relationship require strict calibration procedures or limit the wide applicability of reducedform models due to introducing complexity models involving stochastic processes. The authors propose a notion of the expected recovery rate conditional on the default rate by combining a regression relationship between these two rates and a transformation between default rates under the physical and riskneutral measures. This notion can be simply incorporated into any reduced-form model to simultaneously produce reliable time-varying recovery and default rates. To demonstrate their idea, they revise Jarrow and Turnbull's [1995] reduced-form model used in Chambers and Lu [2007] for pricing convertible bonds. The resulting tree structure is also adjusted to alleviate the infeasible branching probability problem.