The effect of policyholders’ rationality on unit-linked life insurance contracts with surrender guarantees

Abstract

We study the valuation of unit-linked life insurance contracts with surrender guarantees. Instead of solving an optimal stopping problem, we propose a more realistic approach accounting for policyholders’ rationality in exercising their surrender option. The valuation is conducted at the portfolio level by assuming that the surrender rate of the representative agent is bounded from below and from above. The lower bound corresponds to purely exogenous surrender, and the difference between the upper bound and the lower bound represents the rationality of the policyholders. The valuation problem is formulated by a PDE approach and solved with the finite difference method. We show that the rationality of the policyholders has a significant effect on average contract value and hence on the fair contract design. We also present the separating boundary between purely exogenous surrender and endogenous surrender. This provides implications on the predicted surrender activity of the policyholders.