The Effect of Policyholders’ Rationality on Unit-Linked Life Insurance Contracts with Surrender Guarantees

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractWe 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 the surrender intensity to be bounded from below and from above. The lower bound corresponds to purely exogenous surrender and the upper bound represents the limited rationality of the policyholders. The valuation problem is formulated by a valuation PDE 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.

The Effect of Secondary Markets on Equity-Linked Life Insurance with Surrender Guarantees

“…Szimayer [26], but extends their market model by a secondary market on which policyholders may sell their life insurance contracts. The decision behavior of the policyholder of choosing between holding the contract, exercising the surrender option or to sell the contract on the secondary market is a further key component.…”

“…Now, we specify the surrender intensity γ of the representative policyholder for ending the contract following the approach Li and Szimayer [26] that is dating back to Stanton [29].…”

“…Contract valuation in this spirit can be found for example in Albizzati and Geman [1], DeGiovanni [20] and Li and Szimayer [26].…”

“…First, we formulate a financial market augmented for mortality risk. In this market we consider an equity-linked life insurance contract with a surrender option, following Li and Szimayer [26], see also Stanton [29], Dai et al [13], and DeGiovanni [20]. As the second step we extend the setup and add as a new feature the secondary market.…”

“…14 11 The payoff structure is taken from Bernard and Lemieux [5] and also employed by Li and Szimayer [26]. 12 See [5], p. 446.…”