UK fixed rate repayment mortgage indemnity valuation

Abstract

We use a mean-reverting interest rate model and a lognormal house price diffusion model to evaluate British fixed rate mortgage contracts with (embedded) default and prepayment options. The valuation model also provides values for mortgage indemnity guarantees and the corresponding lenders' coinsurance. Since the partial differential equation incorporating the general features of these mortgage contracts does not have a closed-form solution, an explicit finite difference method was used to solve the problem. Changes in contractual features in common mortgage products lead to different equilibrium coupon rates and different values for mortgage components. Our numerical results suggest that mortgage modelling include both of these contractual provisions and the embedded options in order to prevent biased and misleading mortgage valuation.