Modeling Mortgages with Prepayment Penalties

This paper uses a numerical simulation based on the Crank-Nicolson method to estimate the value of a fixed-rate mortgage (FRM) with embedded prepayment and non-defaultable options. We find that the value of the FRM will increase when interest rates decrease, increasing the incentive for borrowers to prepay the mortgage. This paper presents simulated results of prepayment penalties that may help financial institutions enact specific yield maintenance agreements and that may aid financial regulators in providing additional safety for financial lenders and borrowers.