Pricing rate of return guarantees in a Heath-Jarrow-Morton framework

Abstract

Rate of return guarantees are included in many financial products, for example life insurance contracts or guaranteed investment contracts issued by investment banks. The holder of such a contract is guaranteed a fixed periodically rate of return rather than - or in addition to - a fixed absolute amount at expiration. We consider rate of return guarantees where the underlying rate of return is either (i) the rate of return on a stock investment or (ii) the short-term interest rate. Various types of these rate of return guarantees are priced in a general no-arbitrage Heath-Jarrow-Morton framework. We show that despite fundamental differences in the underlying rate of return processes ((i) or (ii)), the resulting pricing formulas for the guarantees are remarkably similar. Finally, we show how the term structure models of Vasicek (1977) and Cox, Ingersoll, and Ross (1985) occur as special cases in our more general framework based on the model of Heath, Jarrow, and Morton (1992).