The Effect of Secondary Markets on Equity-Linked Life Insurance 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 effect of secondary markets on equity-linked life insurance contracts with surrender guarantees. The policyholders are assumed to be boundedly rational in giving up their contracts, and a proportion of policyholders will access the secondary markets instead of surrendering the contracts to the insurance company. We formulate the valuation problems from both the insurance company's and the policyholders' perspectives and characterize the contract values by deriving the respective pricing PDEs. Comparative statics are derived indicating the effect of the level of the policyholder's rationality and secondary market characteristics such as accessibility and competition on the contract values. The pricing PDEs are solved numerically via the Crank-Nicolson scheme to study the implication of the inclusion of a secondary market. We show that a secondary market generally increases the risk borne by the insurance company and the policyholders profit from the secondary market only when the secondary market is sufficiently competitive. Furthermore, we derive the necessary condition for the existence of a fair contract in this context and study the effect of the secondary market on fair contract design.

Life insurance lapse behaviour: evidence from China

“…Most empirical research broadens the meaning of lapse to account for surrender as well as lapse, referring to a lapse in the insurance contract as termination before maturity (Kuo et al 2003;Kiesenbauer 2012;Renshaw and Haberman 1986;Eling and Kiesenbauer 2014). The term surrender usually appears in empirical papers studying the secondary market and in theoretical modelling studies (Kim 2005a, b;Consiglio and De Giovanni 2010;Gatzert 2009;Tsai et al 2002;and Hilpert et al 2014). When using Chinese data, we cannot distinguish lapse behaviour from surrender activity.…”

A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework

“…The policyholder may act optimally with respect to his preferences and circumstances but it may be different from the optimal strategy calculated in (29). On the other hand, as noted in Hilpert et al (2014), secondary markets for equity linked insurance products (where the policyholder can sell their contracts) are growing. Thus, financial third parties can potentially generate guaranteed profit through hedging strategies from financial products such as VA riders which are not priced according to the worst case assumption of the optimal withdrawal strategy.…”

“…Also, as noted in [17], secondary markets for the equity linked insurance products (where the policyholder can sell their contracts) are growing. Thus, third parties can potentially generate a guaranteed profit through hedging strategies from the financial products such as VA riders which are not priced under the assumption of the optimal withdrawal strategy.…”

“…However, the fair fee obtained under the assumption that investors behave optimally to max-imise the value of the guarantee does offer an important benchmark because it is a worst case scenario for the contract writer. Also, as noted in Hilpert et al (2014), secondary markets for equity linked insurance products (where the policyholder can sell their contracts) are growing. Thus, third parties can potentially generate guaranteed profit through hedging strategies from financial products such as VA riders which are not priced under the assumption of the optimal withdrawal strategy.…”

Risk Management of Policyholder Behavior in Equity‐Linked Life Insurance

“…On the one hand, consumers get a better price (lower surrender charges) and on the other hand, it makes the life insurance market more attractive and thus potentially increases the demand for the insurer's products. Hilpert, Li, and Szimayer () further discuss the impact of the surrender option and the existence of a secondary market for equity‐linked life insurance, and show that the introduction of sophisticated investors by the secondary market may lead to higher premiums that account for a higher proportion of optimal surrenders. This result is somewhat consistent with Gatzert, Hoermann, and Schmeiser () who explain that life insurers need to abandon lapse‐supported pricing (i.e., pricing under the assumption of suboptimal lapses that benefit the insurer).…”