A comprehensive model for managing credit risk on home mortgage portfolios

Calibration of the curves for transition probabilities was done with account data for 31,961 mortgages active as of December 1992 and not due to mature during the following year. The aggregate outstanding balances on these loans totaled approximately $5.5 billion. The model was calibrated using transitions among states from a point in time one year to the same point in time the next year to avoid the effects of seasonality and to allow a sufficient accumulation of transitions to the defaulted state for parameter estimation. The logistic functions of models for transitions from a given state were fitted simultaneously using the maximum likelihood criterion. Variables were retained in the transition model if their contributions were statistically significant at the . 1 level for at least one of the logistic functions for transition from a particular state, and if there were no apparent spurious effects that could distort forecasts under alternative economic assumptions. The only exception is the inclusion of unemployment rate for transitions of accounts that are delinquent 30 to 89 days. In this case, the variable was retained, although not statistically significant at the .1 level, because its directional impact conforms to theory. Tables 1 through 3 contain the multinomial logit functions derived for transitions from (1) current, (2) delinquent 30 to 89 days, and (3) delinquent 90+ days, respectively. The statistical significance of the explanatory variables for the individual logit functions (giving the ratios of the logarithms of probabilities of transitions to the delinquent and terminal states relative to probability of transitions to the "current" state) is indicated by a superscript. A positive coefficient means that, ceteris paribus, the average value of the ratio of the transition probabilities increases as the value of the corresponding explanatory variable increases.

The model's complexity makes it difFicult to determine the shape of the transition probability curves from the logistic coefficients alone. To facilitate initial verification and intertemporal comparisons during quarterly recalibration, the fitted models are also presented in graphical format. In Figure 2, we present sample plots of the 15 transition curves that show the effects of varying the loan-to-value ratio while holding all other attributes constant at representative values. Sets of curves illustrating other marginal relationships, such as transition probabilities as a function of loan vintage, unemployment rate, and interest differential are similarly generated. In the early stages of model development, such curves were used to assess the reasonableness of the model's behavior. For example, comparing the subplots of Figure 2, one finds that the highest transition rate to default comes from those loans delinquent 90+ days with high loan-to-value ratios. This is as expected, since the majority of loans pass through the delinquent state before entering foreclosure, and the lack of equity precludes additional borrowing to bring the loan current. In later stages, the curves were used to facilitate understanding of predicted performance under scenarios of interest. Comparisons can be made across several sets of plots (e.g., by generating transition probability curves as functions of loan-to-value for various vintages or geographic regions).