Pricing Dynamic Guaranteed Funds Under a Double Exponential Jump Diffusion Model

Abstract

This paper complements the extant literature to evaluate the prices of dynamic guaranteed funds when the price of underlying naked fund follows a double exponential jump-diffusion process. We first derive the closed-form solution for the Laplace transform of dynamic guaranteed fund price, and then apply the efficient Gaver-Stehfest algorithm of Laplace inversion to obtain the prices of dynamic guaranteed funds. Based on the numerical pricing results, we find that the proposed pricing method is much more efficient than the Monte Carlo simulation approach without losing any accuracy. On the other hand, we also provide an investigation on the behavior of prices of dynamic guaranteed funds when jump is taken into consideration. In addition, the sensitivity analyses of the prices of dynamic guaranteed funds with respect to jump-related parameters are also given in this paper.