A PATH-DEPENDENT APPROACH TO SECURITY VALUATION WITH APPLICATION TO INTEREST-RATE CONTINGENT CLAIMS

The last two decades have witnessed a tremendous growth in the volume of assets and Liabilities whose cash flows depend, in a variety of way s, on the path of interest rates. Some of these, including floating-ra te notes and swap agreements, contractually base cash flows on current and past interest rates and contain caps, floors, and other, more com plex features. Others, including mortgages, many corporate bonds, and time deposits, are fixed-rate instruments that contain embedded option s, such as those to prepay, call, or withdrawal. The irregular exercis e of these options causes cash flows to vary as time proceeds and inte rest rates rise or fall. This paper develops a state-contingent claims technique for valuing such securities. It is derived from the option- based model of Breeden and Litzenberger (1978) using the transition ma trix approach of Banz and Miller (1978). Particular attention is paid to valuing so-called path-dependent securities whose contemporaneous c ash flows depend on the historical path of interest rates as well as t heir current level. A detailed example is provided in which an adjusta ble-rate mortgage is valued under a variety of economic and security s pecific assumptions.