۱- Introduction

۲- Model framework

۳- Contract valuation

۴- Numerical analysis

۵- Conclusion

References

Abstract

We study the risk-neutral valuation of participating life insurance policies with surrender guarantees when an early default mechanism, forcing an insurance company to be liquidated once a solvency threshold is reached, is imposed by a regulator. The early default regulation affects the policies’ value not only directly via changing the policies’ payment stream but also indirectly via influencing policyholder’s surrender. In this paper, we endogenize surrender risk by assuming a representative policyholder’s surrender intensity bounded from below and from above and uncover the impact of the regulation on the policyholder’s surrender decision making. A partial differential equation is derived to characterize the price of a participating policy and solved with the finite difference method. We discuss the impacts of the early default regulation and insurance company’s reaction to the regulation in terms of its investment strategy on the policyholder’s surrender as well as on the contract value, which depend on the policyholder’s rationality level.

Introduction

A typical participating life insurance policy provides policyholders with a minimum interest rate guarantee and bonus payments upon death and upon survival which are linked to the performance of the insurance company. Usually, additional options are embedded in the policies to increase their attractiveness to the policyholders, among which the most popular one is a surrender option. A surrender option entitles the policyholders to terminate their contract prematurely and to obtain the surrender benefits promised by the insurance company. The policyholders may not necessarily receive the payments specified in their contract even if they hold it until maturity. If the insurance company does not have enough reserves to pay back its liabilities at the maturity date, the policyholders cannot get more than what remains in the company. To protect the policyholders from collecting too few benefits as the insurance company declares bankruptcy at maturity, regulatory authorities impose early default mechanisms to monitor insurance companies’ financial status and close them before it is too late. For example, under Solvency II, the supervisory authority withdraws the authorization of an insurance company when its capital falls below the minimum capital requirement and does not recover within a short period of time, see Solvency II Directive (2009/138/EC). Also, an insurance company supervised by the Swiss Financial Market Supervisory Authority (FINMA) can lose its license when its risk-based capital drops below the lowest threshold specified in the Swiss Solvency Test (SST), see FINMA Circ. 08/44 SST, FINMA (2008). Proceeds from liquidated assets are then paid to stakeholders. Hence, the policyholders also face early default risk of the insurance company accompanied with the early default regulatory intervention.