Default Correlation in a Markov-Chain Credit Migration Model with Contagion Effects

In this paper, we extend the earlier results of Jeanblanc and Valchev (2003) in the single name case to the case of multiple defaults of the issuers in a concentrated industry or homo- geneous bond market. We provide solutions for the pairwise default correlations and credit spreads in an intensity-based Markov-chain setting with common macroeconomic factors and firm-specific factors. The base model is extended in two directions. First, we introduce the firm-specific default dependence on the previous defaults on the market in the sense that de- fault of a specific firm changes the generators and the transition probability matrices of the issuer-specific variables of the other firms. Second, we investigate the default dependence when these firm-specific factors are observable in noise. The models can be calibrated to the real data on rating transitions and allow for efficient simulation of portfolio loss distributions.