Grimshaw, Scott D.  and William P. Alexander, "Markov Chain Models for Delinquency: Transition matrix estimation and forecasting", Applied Stochastic Models in Business and Industry, Vol. 27, No. 3, (May/June 2011) , pp. 267-279.

Abstract: A Markov chain is a natural probability model for accounts receivable. For example, accounts that are 'current' this month have a probability of moving next month into 'current', 'delinquent' or 'paid-off' states. If the transition matrix of the Markov chain were known, forecasts could be formed for future months for each state. This paper applies a Markov chain model to subprime loans that appear neither homogeneous nor stationary. Innovative estimation methods for the transition matrix are proposed. Bayes and empirical Bayes estimators are derived where the population is divided into segments or subpopulations whose transition matrices differ in some, but not all entries. Loan-level models for key transition matrix entries can be constructed where loan-level covariates capture the non-stationarity of the transition matrix. Prediction is illustrated on a $7 billion portfolio of subprime fixed first mortgages and the forecasts show good agreement with actual balances in the delinquency states.

Keywords: Delinquency movement matrix, Dirichlet-multinomial posterior, empirical Bayes, loss forecasts, portfolio valuation, roll rates.

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