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Finding Generators for Markov Chains via Empirical Transition Matrices, with Applications to Credit Ratings
Author(s) -
Israel Robert B.,
Rosenthal Jeffrey S.,
Wei Jason Z.
Publication year - 2001
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00114
Subject(s) - markov chain , generator matrix , generator (circuit theory) , stochastic matrix , credit rating , matrix (chemical analysis) , transition (genetics) , econometrics , computer science , transition rate matrix , mathematics , economics , mathematical economics , actuarial science , algorithm , statistics , power (physics) , physics , thermodynamics , chemistry , decoding methods , biochemistry , gene , chromatography
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.