Pricing rate of return guarantees in a heath Jarrow Morton framework

Rate of return guarantees are mcluded in many financial products, for example life insurance contracts or guaranteed investment contracts issued by investment banks. The holder of a such contract is guaranteed s 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 seneral nbarbitrage Heath-Jarrow-Morton framework. We show that there are fundamental differences in the resulting pricmg formulas depending on which of the two types of underlying rate of return ((i) or (ii)) the contract is based on. Finally, we show how the term structure models of Vmicek (1977) and Cox, Ingersall, and Ross (1985) occur as special cases in our more general framework based on the Heath, Jamow, and Morton (1992) model.