Extraction of Implied Default Probabilities
and Expected Recovery Values from a Combination
of Bond Prices and CDS Spreads

Abstract

This article proposes an intuitively simple technique of inferring a term structure of implied default probabilities and a term structure of expected recovery values from a combination of market bond prices and credit default swap spreads. Credit risk for longer maturities can not only be characterized by higher implied default probabilities but also be associated with downward revisions in the expected recovery value. Allowing for a non-flat recovery value term structure along with varying implied default probabilities across different periods can be a useful relaxation of the restriction of a constant recovery rate that is typical to the existing studies on credit risk modeling. We demonstrate that a term structure of recovery values can be separately identified along with the term structure of implied default probabilities through the information contained in the term structure of bond prices and the term structure of credit default swaps with corresponding maturities. Solutions to a set of numerical examples are provided that can be replicated independently. The combination of implied default probabilities and expected recovery values provides a set of valuable tools to value a range of credit claims for which historical default and recovery rates are not readily available.