Bayesian analysis in an aggregate loss model: validation of the structure functions

Common ordinal models, including the ordered logit model and the continuation ratio model, are formulated by a common score (ie, a linear combination of given explanatory variables) plus rank-specific intercepts. Sensitivity to the common score is generally not differentiated between rank outcomes. We propose an ordinal model based on forward ordinal probabilities for rank outcomes. In addition to the common score and intercepts, the forward ordinal probabilities are formulated by the rankand rating-specific sensitivity (for a risk-rated portfolio). This rank-specific sensitivity allows a risk rating to respond to its migrations to default, downgrade, stay and upgrade accordingly. A parameter estimation approach based on maximum likelihood for observing rank-outcome frequencies is proposed. Applications of the proposed model include modeling rating migration probability for point-in-time probability of default term structure for International Financial Reporting Standard 9 expected credit loss estimation and Comprehensive Capital Analysis and Review stress testing. Unlike the rating transition model based on the Merton model, which allows only one sensitivity Print ISSN 1753-9579 j Online ISSN 1753-9587 © 2017 Infopro Digital Risk (IP) Limited 1 Copyright © 2017 Inf i i To subscribe to a Risk Journal visit subscriptions.risk.net/journals or email info@risk.net