Fair Valuation of Participating Life Insurance Contracts with Jump Risk

Abstract

The purpose of this article is to value participating life insurance contracts when the linked portfolio is modeled by a jump-diffusion. More precisely this process has a Brownian component and a compound Poisson one. The jump size is given by a double exponential distribution, so that jumps can be upward as well as downward. More specifically here, the bankruptcy risk of the insurance is considered. Thus market and credit risks are taken into account. Thanks to this modeling, quasi-closed-form formulas are obtained for pricing the life insurance contract at fair value. This allows us to investigate the impact of strategic parameters as well as structural ones, as is shown in the numerical part of this paper. The effects of early default are particularly emphasized.

Keywords: Participating Life Insurance Policies, Kou Processes, Jump-Diffusion, Early Default, Fair Value

JEL Classification: G13, G22