Post by Sapphire Capital on Aug 9, 2008 1:22:46 GMT 4
Information Theoretic Generator Estimation with an Application to Ratings Process Migration
Jeffrey R. Stokes
Pennsylvania St. University
February 2008
Abstract:
The characterization of obligor ratings dynamics as a Markov chain is a common assumption in credit risk modeling. While a continuous time Markov chain is most appealing due to the potential for more robust transition probability estimates, the cost of continuously monitoring obligor ratings can be too high to justify the assumption in practice. For example, banks are more likely to update obligor ratings on a relatively infrequent (e.g. annual) basis making the discrete time Markov chain assumption more tenable in practice. Linking the discrete and continuous Markov chains is a generator matrix that allows for the determination of transition probabilities for any time horizon of interest. Known as the embeddability problem, empirical transition probability estimates for ratings processes rarely posses an exact generator. At least four methods have been proposed for approximating a generator given an empirical transition probability matrix. In this paper, another method is proposed, namely, an econometric model that is flexible, nonparametric, and does not rely on a previously estimated transition probability matrix. Rather, the transition probability matrix is estimated simultaneously with an approximate generator under an information theoretic criterion.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1138654_code91071.pdf?abstractid=1138654&mirid=3
Jeffrey R. Stokes
Pennsylvania St. University
February 2008
Abstract:
The characterization of obligor ratings dynamics as a Markov chain is a common assumption in credit risk modeling. While a continuous time Markov chain is most appealing due to the potential for more robust transition probability estimates, the cost of continuously monitoring obligor ratings can be too high to justify the assumption in practice. For example, banks are more likely to update obligor ratings on a relatively infrequent (e.g. annual) basis making the discrete time Markov chain assumption more tenable in practice. Linking the discrete and continuous Markov chains is a generator matrix that allows for the determination of transition probabilities for any time horizon of interest. Known as the embeddability problem, empirical transition probability estimates for ratings processes rarely posses an exact generator. At least four methods have been proposed for approximating a generator given an empirical transition probability matrix. In this paper, another method is proposed, namely, an econometric model that is flexible, nonparametric, and does not rely on a previously estimated transition probability matrix. Rather, the transition probability matrix is estimated simultaneously with an approximate generator under an information theoretic criterion.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1138654_code91071.pdf?abstractid=1138654&mirid=3