OPTION THEORY AND FLOATING-RATE SECURITIES WITH A COMPARISON OF ADJUSTABLE-RATE AND FIXED-RATE MORTGAGES

This article demonstrates how to value floating-rate securities, in particular adjustable-rate mortgages (ARMs), in the presence of default. The problem is not a straightforward one since endogenous termination (default and prepayment) necessitates solution by backward procedures, but caps on the floating rate then create path dependencies. The solution is to introduce an artificial state variable, the past contract rate, in addition to the natural stochastic variables, the interest and the house price process. With this technique, a numerical investigation of the properties of defaultable ARMs is provided. In all cases, a comparison is made with standard fixed-rate mortgages.