Abstract:
We develop a model, similar to the model developed by Jou and Lee (2011), to calculate the optimal penalty a lender should charge as compensation for the loss due to prepayment of a fixed rate mortgage. The lender should charge a penalty fee to reduce the deterioration of returns when borrowers replace older higher interest rate mortgages with new, lower interest rate mortgages. By assuming the value of a floating rate mortgage equals the value of a fixed rate mortgage plus the prepayment option, we set the maximum value of the prepayment option as the optimal penalty. So that the diverging factor between the two types of mortgages is that a fixed rate mortgage is embedded with the option to prepay. We assume that the optimal penalty incorporates two forms of compensation, one being the mortgage rate differential and the other being a penalty fee as a percent of the principal. Using the Monte Carlo technique we calculate the expected optimal penalty and analyse how key determinants in the model affect the expected optimal penalty. We find it’s optimal for a lender to charge a higher prepayment penalty when the maturity of the mortgage is longer, and the volatility and speed of adjustment of mortgage rates is greater. The relationship with the speed of adjustment, in particular, depends on the initial direction of the mortgage rate curve on average. Specifically, a rising (decreasing) mortgage rate curve produces a negative (positive) effect between the speed of adjustment and the total optimal penalty. Lastly, we find the Cox-Ingersoll-Ross (CIR) mean-reverting model in comparison to the Vasicek mean-reverting model, as the better model as it produces more realistic values of the optimal penalty.