Stochastic models were developed that provide important measures related to retail mortgages and credit cards for the management of a bank. Based on Markov theory, two models were developed that predict mortgage portfolio size and expected duration of stay in each of the states, which are defined according to the criteria of Basel Accord II and the Federal Reserve Bank. Also, to facilitate comparisons among different types of credit products and different time periods, a model was developed to generate a health index for a retail mortgage. This model could be easily extended, using multivariate regression or multivariate time series techniques, to analyze the interaction between a mortgage and local macroeconomic factors. Furthermore, the models in this dissertation address decision making on the part of the management of a bank concerning business strategy such as collection policies and loan officer compensation policies. Extending the basic assumption of the Markov property to a higher-order Markov model and a multivariate Markov model, this work also analyzed the correlation between the payment pattern for retail mortgages and credit cards. To complete this correlation analysis, a comparison among 3 models (higher-order, multivariate, and a higher-order multivariate Markov model (HMMM)) has also been provided. Finally, an interaction analysis between the payment behavior of a retail mortgage and local macroeconomic variables has been performed using an Interactive Hidden Markov Model (IHMM). For IHMM and HMMM models, the number of unknown parameters increases exponentially with the increase of the order of the models. Hence, to deal with this situation, a linear programming algorithm has been used to obtain solutions for the HMMM and IHMM.

The models provided in this study are of practical importance to the bank management. Not only do they give quantitative measures about loan stand-alone characteristics, but also they provide cross-section comparisons among different credit products and multi-period loan performance tracking as well. These models, used to analyze retail mortgages and credit cards, could be easily applied to other credit products issued by a commercial bank.

The data used in this study have been obtained from an Ohio local commercial bank. It includes monthly paid 20-year retail mortgages and personal credit cards. A contract has also been signed to guarantee that the data would be used only for academic research.