Optimal Surrender Policy for Variable Annuity Guarantees

Bernard, Carole; MacKay, Anne; Muehlbeyer, Max

doi:10.2139/ssrn.2352572

Cited by 14 publications

(51 citation statements)

References 23 publications

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“…We assume that the total fee withdrawn from the VA account throughout the term of the contract is set as the sum of a fixed percentage c of the account value, and a deterministic, pre-determined amount p t at time t (in other words, the deterministic amount does not need to be constant). 2 Our paper constitutes a significant extension of the results obtained on the optimal surrender strategy for a fee set as a fixed percentage of the fund [4], since the deterministic fee structure increases the complexity of the dynamics of the VA account value. For this reason, we need to resort to PDE methods to obtain the optimal surrender strategy 1 Specifically, the policyholder has the option to surrender the contract and to receive a "surrender benefit", which can be more valuable than the contract itself.…”

Section: Introductionmentioning

confidence: 81%

“…Setting p t = 0, we will find back the results commonly used in the literature with the fee being only paid as a percentage of the fund (see for example [4]). …”

Section: Variable Annuitymentioning

confidence: 89%

“…As in [4,13], we assume that the policyholder has the option to surrender the policy at any time t and to receive a surrender benefit at surrender time equal to…”

Section: Benefitsmentioning

confidence: 99%

“…For this reason, we need to resort to PDE methods to obtain the optimal surrender strategy 1 Specifically, the policyholder has the option to surrender the contract and to receive a "surrender benefit", which can be more valuable than the contract itself. This additional value, as well as the optimal surrender strategy, is explored and quantified by Bernard, MacKay, and Muehlbeyer in [4] in the case when the fees are paid as a percentage of the underlying fund. 2 Note that the deterministic amount component of the fee can be interpreted as a variable percentage of the account value F t .…”

Section: Introductionmentioning

confidence: 99%

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Reducing Surrender Incentives Through Fee Structure in Variable Annuities

Bernard

MacKay

2015

Innovations in Quantitative Risk Management

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In this chapter, we study the effect of the fee structure of a variable annuity on the embedded surrender option. We compare the standard fee structure offered in the industry (fees set as a fixed percentage of the variable annuity account) with periodic fees set as a fixed, deterministic amount. Surrender charges are also taken into account. Under fairly general conditions on the premium payments, surrender charges and fee schedules, we identify the situation when it is never optimal for the policyholder to surrender. Solving partial differential equations using finite difference methods, we present numerical examples that highlight the effect of a combination of surrender charges and deterministic fees in reducing the value of the surrender option and raising the optimal surrender boundary.

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Section: Introductionmentioning

confidence: 81%

“…Setting p t = 0, we will find back the results commonly used in the literature with the fee being only paid as a percentage of the fund (see for example [4]). …”

Section: Variable Annuitymentioning

confidence: 89%

“…As in [4,13], we assume that the policyholder has the option to surrender the policy at any time t and to receive a surrender benefit at surrender time equal to…”

Section: Benefitsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Reducing Surrender Incentives Through Fee Structure in Variable Annuities

Bernard

MacKay

2015

Innovations in Quantitative Risk Management

Self Cite

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“…Marshall et al (2010) studied the valuation of a guaranteed minimum income benefit (GMIB). Bernard et al (2014) proposed models for optimal surrender strategy for various guaranteed benefits with surrender options. However, less is known with regard to the risk management of these guaranteed benefits.…”

Section: Introductionmentioning

confidence: 99%

Comonotonic approximations of risk measures for variable annuity guaranteed benefits with dynamic policyholder behavior

Feng

Jing

Dhaene

2017

Journal of Computational and Applied Mathematics

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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 AbstractThe computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed benefits. The current market practice of Monte Carlo simulation often requires intensive computations, which can be very costly for insurance companies to implement and take so much time that they cannot obtain information and take actions in a timely manner. In an attempt to find low-cost and efficient alternatives, we explore the techniques of comonotonic bounds to produce closed-form approximation of the risk measures for variable annuity guaranteed benefits. The techniques are further developed in this paper to address in a systematic way risk measures for death benefits with the consideration of dynamic policyholder behavior.

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Piecewise linear boundary crossing probabilities, barrier options, and variable annuities

Lee

2022

Journal of Futures Markets

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Barrier options have been instrumental in satisfying various market demands. This paper introduces piecewise linear barrier options and provides their pricing formulas. To this end, we establish the analytical piecewise linear boundary crossing probability and explain how to approximate arbitrary boundary crossing probabilities. In addition, we show that a financial instrument with early exercise is decomposable into a knock‐out barrier option and immediate rebate, which casts a new illumination of the value of early exercise. We consider a variable annuity with guaranteed minimum accumulation benefit rider and surrender option to illustrate the decomposition. Extensive numerical experiments validate theoretical findings.

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Optimal Surrender Policy for Variable Annuity Guarantees

Cited by 14 publications

References 23 publications

Reducing Surrender Incentives Through Fee Structure in Variable Annuities

Reducing Surrender Incentives Through Fee Structure in Variable Annuities

Comonotonic approximations of risk measures for variable annuity guaranteed benefits with dynamic policyholder behavior

Piecewise linear boundary crossing probabilities, barrier options, and variable annuities

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