Finite difference approach to the valuation and prepayment strategy of mortgages

Abstract

This paper studies the value of mortgage contract by assuming the market interest rate follows the Cox-Ingersoll-Ross (CIR) model and correspondingly the borrower's optimal strategy to make prepayment. The problem is formulated as a partial differential equation with initial and boundary conditions imposed by the contract conditions. Finite difference approach is applied to solve (1) the optimal prepayment interest rate; (2) the value of the mortgage contract when prepayment is allowed. In addition, numerical solutions are verified with analytical asymptotic results for the small volatility scenario.