On the Valuation of GMDB Options Using a Combination of Exponentials

This paper explores the applicability of a combination of exponentials to the valuation of guaranteed minimum death benefits (GMDBs) embedded in variable annuities. As is well known, the class of combinations of exponentials forms a weakly dense subset among the distributions of all nonnegative random variables. Moreover, explicit pricing formulas for various GMDBs are available under a simplified exponential mortality model. Motivated by these two facts, we first approximate the future lifetime distributions by using a combination of exponentials and then approximate GMDB option prices. Comparing with the numerical integration under the Makeham law of mortality, our numerical result shows that the approximation can be quite useful.