Pricing Rate Caps on Default-Free Adjustable-Rate Mortgages

A model is developed and utilized in this paper to value a life of loan interest rate cap on an ARM that reprices monthly. The value of the cap is seen to depend importantly on both the slope of the term structure and the variance of the one month rate. However, the cap value is not sensitive to the source of the slope of the term structure -- what precise combination of interest rate expectations and risk aversion determined the slope. This insensitivity is fortunate because of the great difficulty of knowing at any point in time why the term structure is what it is. Given the variation in the slope of the term structure and the variance of the one month rate that occurred over the 1979-84 period, the addition to the coupon rate on a one-month ARM that lenders should have charged for a 5 percent life of loan cap has ranged from 5 to 40 basis points.