Building Models for Credit Spreads

One standard approach to analyzing credit derivatives is to set up a Markov transition matrix describing the probabilities of moving one credit class, e.g., the Moody's bond rating, to another, and potentially to a state of default. Models based on credit migration matrices have generally been rather limited in their ability to capture real-world features of credit-sensitive instruments, such as correlation between default probabilities and interest rate movements, stochastic but correlated rate spreads between credit classes, stochastic recovery rates, and within class-yield differences that depend on whether a given bond has been upgraded or downgraded. This article presents a useful general family of credit spread models that can be set up to incorporate each of these features.