Optimal Interest Rate for a Borrower with Estimated Default and Prepayment Risk Optimal Interest Rate for a Borrower with Estimated Default and Prepayment Risk

by Howard, Scott T

Today's mortgage industry is constantly changing, with adjustable rate mortgages (ARM), loans originated to the so-called "subprime" market, and volatile interest rates. Amid the changes and controversy, lenders continue to originate loans because the interest paid over the loan lifetime is profitable.

Measuring the profitability of those loans, along with return on investment to the lender is assessed using Actuarial Present Value (APV), which incorporates the uncertainty that exists in the mortgage industry today, with many loans defaulting and prepaying. The hazard function, or instantaneous failure rate, is used as a measure of probability of failure to make a payment. Using a logit model, the default and prepayment risks are estimated as a function of interest rate. The "optimal" interest rate can be found where the profitability is maximized to the lender.