A CB (corporate bond) pricing probabilities and recovery rates model for deriving default probabilities and recovery rates

In this paper we formulate a corporate bond (CB) pricing model for deriving the term structure of default probabilities (TSDP) and the recovery rate (RR) for each pair of industry factor and credit rating grade, and these derived TSDP and RR are regarded as what investors imply in forming CB prices in the market at each time. A unique feature of this formulation is that the model allows each firm to run several business lines corresponding to some industry categories, which is typical in reality. In fact, treating all the cross-sectional CB prices simultaneously under a credit correlation structure at each time makes it possible to sort out the overlapping business lines of the firms which issued CBs and to extract the TSDPs for each pair of individual industry factor and rating grade together with the RRs. The result is applied to a valuation of CDS (credit default swap) and a loan portfolio management in banking business.