Monotonicities in a Markov Chain Model for Valuing Corporate Bonds Subject to Credit Risk

In recent years, it has become common to use a Markov chain model to describe the dynamics of a firm's credit rating as an indicator of the likelihood of default. Such a model can be used not only for describing the dynamics but also for valuing risky discount bonds. The aim of this paper is to explain how the Markov chain model leads to the known empirical findings such that prior rating changes carry predictive power for the direction of future rating changes and a firm with low (high, respectively) credit rating is more likely to be upgraded (downgraded) conditional on survival as the time horizon lengthens. The model will also explain practically plausible statements such as that bond prices as well as credit risk spreads would be ordered according to their credit qualities. Stochastic monotonicities of absorbing Markov chains play a prominent role in these issues.