Calibration of PD Term Structures: To Be Markov Or Not To Be

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 proba-bilities 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 time-continuous Markov chain to observed one-year rating migrations and multi-year default frequencies, hereby achieving convincing approximation quality. 1 Markov Chains in Credit Risk Modeling The probability of default (PD) for a client is a fundamental risk parameter in credit risk man-agement. It is common practice to assign to every rating grade in a bank’s masterscale a one-year PD in line with regulatory requirements; see [1]. Table 1 shows an example for default frequencies assigned to rating grades from Standard and Poor’s (S&P).