UK Fixed Rate Repayment Mortgage and Mortgage Indemnity Valuation
使用均值回归利率模型和对数正态房价扩散模型，评估包含违约和提前还款期权的英国固定利率抵押贷款合同，并计算抵押赔偿担保及贷款人剩余风险暴露。
We use a mean‐reverting interest rate model and a lognormal house price diffusion model to evaluate British fixed rate repayment mortgage contracts with (embedded) default and prepayment options. The model also provides values for capped mortgage indemnity guarantees and the corresponding (residual) lender’s 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 is used for the valuation (and sensitivity) results, with solution improvements to deal with error bounds. Then we provide graphical representations of each mortgage component as a function of house prices and interest rate levels, along with interpretations of the analysis. We calculate precisely the lender’s (residual) exposure to house price risk, given the borrower’s options, house and interest rate uncertainty, and customary mortgage indemnity insurance for high loan/collateral ratio mortgages.