Calibration of PD Term Structures: To be Markov or not to be

by Christian Bluhm of Credit Suisse, and
Ludger Overbeck of the University of Giessen

November 2007

Abstract: Term structures of default probabilities are omnipresent in credit risk modeling: time-dynamic credit portfolio models, default times, and multi-year pricing models, they all need the time evolution of default probabilities as a basic model input. Although people tend to believe that from an economic point of view the Markov property as underlying model assumption is kind of questionable it seems to be common market practice to model PD term structures via Markov chain techniques. In this paper we illustrate that the Markov assumption carries us quite far if we allow for nonhomogeneous time behaviour of the Markov chain generating the PD term structures. As a 'proof of concept' we calibrate a nonhomogeneous continuous-time Markov chain (NHCTMC) to observed one-year rating migrations and multi-year default frequencies, hereby achieving convincing approximation quality.

Keywords: Default Probabilities, Term Structure, Nonhomogeneous Markov Chain.

Published in: RISK, Vol. 20, No. 11, (November 2007), pp. 98-103.

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