Early Default Risk and Surrender Risk: Impacts on Participating Life Insurance Policies

We study the fair valuation of participating life insurance policies with surrender guarantees when an early default mechanism is imposed by a regulator. An insurance company is forced to be liquidated once a solvency threshold is reached before maturity. The early default regulation affects the contracts’ value not only directly via changing the contracts’ payment streams but also indirectly via influencing policyholders’ surrender behaviors. In this paper, we endogenize surrender risk by assuming a representative policyholder’s surrender intensity bounded from below and from above and uncover the impacts of the regulation on the policyholders’ surrender decision making. A partial differential equation is derived to characterize the price of a participating policy and solved with the finite difference method. Finally, we discuss the impacts of early default regulation and insurance company’s investment strategies on the policyholder’s surrender behavior as well as on the contract value, which are dependent on policyholder’s rationality level.