A Markov Chain Modeling Approach for Predicting a Retail Mortgage Health Index

ABSTRACT This paper provides an indexing procedure for a mortgage loan health status by means of a finite Markov chain approach, which converts the loan health abstract idea into a workable number system. This method could be easily extended to other banking products as well. A regression method is used to analyze the local macroeconomic factors' effect on the health index. The management of a bank could use these procedures to adjust its loan approval policies based on current characteristics and future prediction of the portfolio. (ProQuest: ... denotes formulae omitted.) INTRODUCTION An index system for the quality or health of a portfolio enables the management of a commercial lending institute to analyze the performance of its portfolio as well as its credit policy over time. Furthermore, this system should provide dynamic description of a portfolio's payment behaviors so that the management could not only have a static snapshot of credit assets' status, but also the dynamic risk characteristics. In other words, it should give the management an analytic tool to measure the credit risk over time by analyzing and predicting the transition behavior among the different states of the loan and calculating the health index of the loan. In this paper, we use a finite Markov chain approach to provide an indexing procedure by which one can monitor the health status of a mortgage loan over time. LITERATURE REVIEW There are many quantitative methods in credit asset management. (White, 1993) surveyed some models employed in the banking industry. The models include discriminant analysis, decision tree, expert system for static decision, dynamic programming, linear programming, and Markov chains for dynamic decision models. Which model is best depends on the situation and the purpose of the analysis. However, in the analysis of credit risk and selection of optimal policy, the standard approach is to use stochastic models based on Markov transition matrices, aided by dynamic programming. As summarized by (White, 1993), Markov decision models have been used extensively to analyze real world data in (1) Finance and Investment, (2) Insurance, and (3) Credit area. Consumer credit analysis is used to analyze account receivable, as triggered by credit sales. A model, based on the transition probability between different states, is primarily used by a company to adjust its credit sale and collection policy. Absorbing states could be reached either by collection or bad debt, both of which lead to a decline in the portfolio size. On the other hand, by defining a past-due period as a different transient state, and default as an absorbing state, Markov models are used to analyze the characteristics of a loan portfolio, namely the estimated duration before an individual defaults, prediction of economic portfolio balance, and health index. Cyert, Davidson and Thompson (1962) developed a finite stationary Markov chain model to predict uncollectible amounts (receivables) in each of the past due category. This classic model is referred to as the CDT model. The states of the chain (Sj,-j=0,l,2, ...,N) were defined as normal payment, past due, and bad-debt states. The probability Py of a dollar in state i at time t transiting to state j at time t + 1 is given as: where B tj is the amount in state J at time t+1 which came from state i in the previous period. S1=S0Q is the vector whoseyth component is the amount outstanding for they'th past due category at the beginning of the fth period for t=l,2, ...,. Here, s is a sub-matrix, in the transition probability matrix Py=[I O; R Q], which includes transition probabilities among the set of transient states. Criticizing the appropriateness of the stationary Markov chain model of (Cyert, Davidson & Thompson, 1962), (Frydman, Kallberg & Li Kao, 1968) applied a mover-stayer Model as an alternative. They defined they step transition matrix of this model as P(0,j)=SI+(I-S)MJ, where M=(mik) is a transition probability matrix for "movers" from i to k, and S = diag(sj,s2,. …