Estimating Future Transition Probabilities when the Value of Side Information Decays, with Applications to Credit Modeling
Journal of Risk Volume 14/Number 1, Fall 2011
38 Pages Posted: 26 Mar 2010 Last revised: 9 May 2012
Date Written: March 17, 2010
A number of conditional transition probability models make use of side information - explanatory variable values known only initially and useful for predicting transitions of the variables of interest. For example, the Cox Proportional Hazard Model is used to provide future hazard arrival probabilities based on initially available side information. In this paper, we observe that a number of commonly used models, including the Cox Proportional Hazard model, force the side information value (which we define precisely) to persist over all time horizons, in contradistinction to evidence, drawn from historical data, indicating that the value of side information, in fact, exhibits pronounced decay over time. There is a solid intuition behind this decay: explanatory variable values typically evolve over time, so the incremental predictive value of the initially available side information should decline over time. Using information - theoretic methods, we introduce new, tractable and robust methods to estimate conditional transition probability models that enforce decay in information value. That is, under our models, the impact of the explanatory variables on the conditional probability distribution must decay over time. We benchmark our methods against other methods on Compustat default transition data and Standard & Poor’s Rating transition data; here, the side information consists of initial observations of financial ratios and other explanatory variables. We find that our methods outperform the benchmark methods out-of-sample.
Keywords: Transition probability model, side information, information value decay, credit model, hazard rate model, default probability model, rating transition model, information theory, minimumrelative entropy principle, conditional relative entropy, robust model
JEL Classification: C13, C14, C51, C53
Suggested Citation: Suggested Citation