Affine Markov chain model of multifirm credit migration

Abstract

This paper introduces and explores a natural extension of the Chen–Filipovic affine models for credit migration, credit spreads and credit default correlation. The essential addition proposed here is to introduce a Markov chain for the “credit rating” of each firm, which are independent conditioned on a stochastic time change. The stochastic time change is then combined with other stochastic factors, here the interest rate and the recovery rate, into a multidimensional affine process. The resulting general framework has the computational effectiveness of the Chen–Filipovic models, but without certain of their conceptual drawbacks. This paper, as the first of the series, aims to illustrate the potential of the general framework by exploring a minimal implementation which is still capable of combining stochastic interest rates, stochastic recovery rates and the multifirm default process. Already within this minimal version we see very good reproduction of essential features such as credit spread curves, default correlations and multifirm default distributions. 1This research was supported by the Natural Sciences and Engineering Research Council of Canada and the MITACS National Centre of Excellence, Canada.