Impacts of Jumps and Stochastic Interest Rates on the Fair Costs of Guaranteed Minimum Death Benefit Contracts

The authors offer a new perspective to the domain of guaranteed minimum death benefit contracts. These products have the particular feature to offer investors a guaranteed capital upon death. The authors propose a complete methodology illustrated by a numerical analysis based on Fast Fourier Transform. New results are given in this paper and as a by product, we give the way to price options in a non Gaussian economy with stochastic interest rates. This paper extends Milevsky and Posner (2001). In contrast to their results, the fair costs of the guarantee feature are found to be substantially higher in this more general economy