Pricing variable annuity with surrender guarantee

Abstract

In this paper we present a variable annuity (VA) contract embedded with a guaranteed minimum accumulated benefit rider that can be chosen to surrender the contract anytime before the maturity. In contrast to the model considered by Bernard et al. (2014), the surrender benefit in our problem is linked to the maximum value between the policyholder’s account value and the guaranteed minimum accumulated benefit. Thus, the surrender benefit of our model provides a protection against the downside risk of financial market throughout the life of contract, and thus it can be referred to as surrender guarantee. Under this circumstance with surrender guarantee, the VA contract has double surrender regions, that is, there exist two optimal surrender boundaries such that if the policyholder’s account value hits one of these boundaries, then the policyholder immediately surrenders the VA contract. Based on the Mellin transform techniques, we derive the coupled integral equations for the two optimal surrender boundaries. We solve numerically these coupled integral equations by using the recursive integration method and provide comparative statics analysis with respect to various parameters.