The pricing of FIREARMs (“Falling Interest Rate Adjustable-Rate Mortgages”)

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Abstract

The purpose of this article is to propose and price a new type of adjustable-rate mortgage: the FIREARM (“Falling Interest Rate Adjustable-Rate Mortgage”). The interest payments on this mortgage adjust downward whenever interest rates decline, while remaining stable when interest rates increase. The FIREARM is alternatively priced as a prepayable and non-prepayable mortgage with a spread over the short-term interest rate. We price these two instruments and contrast their prices with those of fixed-rate mortgages using the parsimonious assumptions of a non-stationary arbitrage-free binomial term structure model.