Multi-Period Structural Model of Mortgage Portfolio with Cointegrated Factors

We propose a new dynamic two-factor model of a loan portfolio. Following the common approach, we quantify the credit risk associated with the portfolio by the probability of default and the loss given default, each of which is driven by a factor common for all debts in the portfolio, and a factor individual to each debt. In line with the empirical evidence, the individual factors are assumed to be AR(1) processes. The common factors, on the other hand, may be dependent on the external (macroeconomic) environment. We apply our model to the US nationwide mortgage portfolio, fitting the dynamics of the factors with a VECM model with several macroeconomic indicators as exogenous variables.