Numerical solution of a two state variable contingent claims mortgage valuation modelªᵇ

Abstract

Previously published work on mortgage component valuation has concentrated on the US market and is inapplicable to some of the mortgage arrangements outside of that market. We model UK repayment mortgages with capped Mortgage Insurance Guarantees (which affect both the equilibrium lending rates and the lender's residual exposure). A contingent claims framework is developed, with an explicit finite differences solution. Then the mortgage components are valued, assuming arrangement fees but no prepayment penalties, under various scenarios, and also under equilibrium conditions: The transformation of the original PDE, and the details of the finite difference solution are given, along with graphical sensitivities of the mortgage participants (including the options held or written by the borrower, the insurer, and the lender) to interest rates and house prices