Finding Generators for Markov Chains via Empirical Transition Matrices, with Applications to Credit Ratings

Authors: Israel, Robert B.¹; Rosenthal, Jeffrey S.²; Wei, Jason Z.³

Source: Mathematical Finance, Volume 11, Number 2, April 2001 , pp. 245-265(21)

Buy & download fulltext article:

Price: $48.00 plus tax (Refund Policy)

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.

Keywords: generators; Markov chains; Markov processes; transition matrix; credit rating

Document Type: Research article

DOI: http://dx.doi.org/10.1111/1467-9965.00114

Affiliations: 1: Department of Mathematics, University of British Columbia, 2: Department of Statistics, University of Toronto, 3: Division of Management, University of Toronto at Scarborough

Publication date: 2001-04-01