A Multi-Factor, Markov Chain Model for Credit Migrations and Credit Spreads

This paper develops and implements a multi-factor, Markov chain model for bond rating migrations and credit spreads. The building blocks are historical transition matrixes and a set of latent credit cycle variables. The model’s central feature is for transition matrixes to be time-varying, and driven by rating-specific latent variables which encompass such economic factors as the business cycle. The paper weaves together the credit risk modeling and the valuation procedures via linking the observed and risk-neutral transition matrixes by the estimated risk premiums, and allows credit derivatives to be priced thereof. The main contributions can be summarized as follows. First, the paper proposes a model for bond rating transitions that incorporates well documented empirical properties of transition matrixes such as their dependence on business / credit cycles. The model also allows for inter-rating variations in credit quality changes. Second, unlike many studies which focus solely on empirical modeling of rating transitions or default rates, this paper shows how the empirical model can be implemented for actual valuations. Third, the estimation and calibration procedures are easy to follow and implement. Other than the historical transition matrixes, the only other data required are bond prices. Preliminary empirical results show, among other things, that allowing for inter-rating variations in credit quality changes via a multi-variate model can substantially improve the goodness of fit.