# 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
### Abstract

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.
### Download:

.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: