The Valuation of Mortgages With Partial Prepayment Risk Under the Equal Principal Payment Method

ABSTRACT This article develops a valuation model for mortgages with partial prepayment risk under the equal principal payment method. To model partial prepayment, we assume prepayment events occur at the jump times of a point process. The proportion of the prepayment amount to the outstanding principal balance is characterized by a stochastic process. By defining specific forms for the point process and stochastic process, we derive explicit valuation formulas for the mortgage loan. Finally, after resolving the computational challenge of multiple integrals via matrix exponentiation techniques, numerical results are presented to investigate the impact of some parameters on the valuation.