Mapping the drift to default: a credit risk modelling approach to the early termination of UK residential mortgages
Kay, Steven Frank
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This thesis is devoted to UK Mortgage Performance Modelling. The research conducted uses an option pricing methodology to model theoretically the value of Mortgages, the Option to default and the probability to default and to compare the predictive accuracy of the latter with the predictive accuracy of data driven credit-scoring techniques. Theoretical models are constructed to represent the life cycles of loans collateralised by real property operating within a stochastic economic environment of house-price and interest rate. These realistic mortgage models provide a confirmation of recent research based upon a relaxation of the assumption of financially rational, 'ruthless' prepayment, bridge a potential oversight in existing research by an extension of existing modelling in the stochastic behaviour of the house price process and present a proposal for a straightforward approach utilising characteristic measures of borrower delinquency and insolvency that enables estimation of the default probabilities implicit in residential mortgages using a simple but enhanced optimising structural model. This model straightforwardly demonstrates that one can predict the probability of eventual default, beginning at the origination of the loan, the time when a lender would be most interested in making such a determination. Secondly the problem of mortgage loan default risk is empirically assessed in a number of different ways focusing upon analysis of the competing risks of early termination, the inclusion of macro-economic variables - time varying covariates and unobserved borrower heterogeneity. Key insight is provided by means of a multi-period model exploiting the potential of the survival analysis approach when both loan survival times and the various regressors are measured at discrete points in time. The discrete-time hazard model is used as an empirical framework for analysing the deterioration process leading to loan default and as a tool for prediction of the same event. Results show that the prediction accuracy of the duration model is better than that provided by a single period logistic model. The predictive power of the discrete time survival analysis is enhanced when it is extended to allow for unobserved individual heterogeneity (frailty).