Application of survival analysis to cash flow modelling for mortgage products

In this article, we describe the construction and implementation of a pricing model for a leading UK mortgage lender. The crisis in mortgage lending has highlighted the importance of incorporating default risk into such pricing decisions by mortgage lenders. In this case the underlying default model is based on survival analysis, which allows the estimation of month-to-month default probabilities at a customer level. The Cox proportional hazards estimation approach adopted is able to incorporate both endogenous variables (customer-specific attributes) and time-covariates relating to the macro-economy. This allows the lender to construct a hypothetical mortgage portfolio, specify one or more economic scenarios, and forecast discounted monthly cash flow for the lifetime of the loans. Monte Carlo simulation is used to compute different realisations of default and attrition rates for the portfolio over a future time horizon and thereby estimate a distribution of likely profit. This differs from a traditional scorecard approach in that it is possible to forecast default rates continually over a time period rather than within a fixed horizon, which allows the simulation of cash flow, and differs from the company's existing pricing model in incorporating the possibilities of both default and early closure.