The major objective of this paper is to identify conditions under which a true generator can or cannot exist for an empirically observed transition matrix. In this study, an approach to finding a valid generator has been presented and the signs to look for, when trying to choose the ‘correct’ generator, have been forwarded. Conditions for the estimation of an approximate generator when a true generator does not exist have also been explored in this paper. Finally, we have given illustrations using transition matrices published by CRISIL.

Credit rating transition matrices have received widespread attention since the seminal work by Jarrow et al. (1997) for the purposes of credit risk modelling. An improvement on the estimation procedure was provided by Kijima and Komoribayashi (1998). A framework within which credit rating migrations can exhibit the usual empirical regularities was developed by Arvanitis et al. (1999). Lando (2000) then showed how a transition matrix can be used to value credit derivatives such as a default swap in an important note.

Rating transition matrices have also received increasing attention in the financial industry with two major bond rating services in the United States, i.e., Moody’s and Standard and Poor’s along with their subsidiaries in other countries, now publishing an annual update of historical transition matrices, together with a wealth of other related information. The shortest time interval within which a transition matrix is usually estimated is one year with the number of transition observations within a shorter period too small for a reliable transition matrix to be estimated.

Applied Finance Journal, Generator Estimation for Transition Matrices, Applications to Credit Ratings