A Fixed-Rate Mortgage Valuation Model in Three State Variables

Abstract

This article investigates the effect of a two-factor interest rate process on the value of the mortgage and its inherent options including the right to default. Our complete three-state model for a mortgage derivative asset is used to make comparisons with the standard two-state model with the option to default or prepay. With slight modification, this model is applicable to other types of mortgages and mortgage-backed securities, and to derivative securities in general. The authors demonstrate that a two-state model with a one-factor term structure and a three-state model with a two-factor term structure value a mortgage substantially differently. The results suggest that valuing defaultable mortgages requires a three-state option pricing model to avoid mispricing.