An Intensity Based Non-Parametric Default Model for Residential Mortgage Portfolios

Abstract

In June 2003 Swiss banks held over CHF 500 billion in mortgages. This important segment accounts for about 63% of all loan portfolios of Swiss banks. Since default insurance is not common in Switzerland, the corresponding risks are a severe threat for the health of the financial system. We focus the analysis on portfolios of residential mortgages and model the probability distribution of the number of defaults using a non-parametric approach, where the intensity processes associated to the time-to-default is linked to a set of predictors through general smooth functions: A generalized additive model is used to condition default intensities of mortgages on relevant economic risk drivers. We calibrate our model on a large mortgage servicing data set and compare the resulting loss distributions to a well-known benchmark, i.e. the loss distribution from CreditRisk+ as commonly applied in the industry. The conditional loss distribution and risk measures for a large mortgage portfolio are shown to be greatly sensitive to the prevailing socio-economic scenario. We present evidence that aggregated res- idential mortgage default risk is not only driven by the rating but also by variables such as the loan-to-value ratio, contract age, regional unemployment as well as contract rate changes and the contract type. Hence, it is crucial to integrate the significant factors into any reasonable bank risk, portfolio or capital management framework or approaches for structuring and pricing of related products. We illustrate the severe shortcomings of the unconditional ap- proaches. With our results we are able to contribute significantly to the ongoing international discussion about the drivers of residential mortgage risk as well as to suggestions for improved risk management approaches. Finally, our findings are highly relevant for the implementation of the Basel II accord. Keywords: reduced-form, structural approach, default risk, default intensity, mortgages, generalized additive model, CreditRisk+.