Building Models for Credit Spreads

This article shows how a modeling framework for the evolution of credit spreads can be built up starting from a simple representation with only two states - default and no default. The model is generalized by introducing credit classes, with transitions from one class to another driven by a deterministic credit migration matrix to account for credit rating behavior. The model allows memory in credit rating changes, credit spread volatility, and mean reversion. This framework allows the derivation of explicit pricing formulas for risky bond and bond option prices, which facilitates implementation and calibration. The credit migration matrix is calibrated on observed bond prices of various credit ratings and uses the Moody's historical credit migration matrix. The authors present examples based on real market data and make some empirical assessment of the model specification using historical time series