Finding Generators for Markov Chains via Empirical Transition Matrices,

with Applications to Credit Ratings

by Robert B. Israel, Jeffrey S. Rosenthal, and Jason Z. Wei

Mathematical Finance 11 (2001), 245-265


In this paper we identify conditions under which a true generator does or does not exist for an empirically observed Markov transition matrix. We show how to search for valid generators and choose the "correct" one that is the most compatible with bond rating behaviors. We also show how to obtain an approximate generator when a true generator does not exist. We give illustrations using credit rating transition matrices published by Moody's and by Standard and Poor's.


.dvi file , PostScript file, Adobe .pdf file

Maple program by Robert B. Israel

generator is a Maple program to find generators for continuous-time Markov chains with a given time-1 transition matrix, as outlined in the paper.

Make sure you get the correct version, corresponding to which release of Maple you use: