Valuation of Guaranteed Minimum Maturity Benefits in Variable Annuities with Surrender Options

Shen, Yang; Sherris, Michael; Ziveyi, Jonathan

doi:10.2139/ssrn.2695265

Cited by 3 publications

(17 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The fees typically covers ongoing costs associated with keeping the policyholder invested in the fund, transaction costs associated with buying and selling assets in the fund, and some advisory fees. In this paper, we assume a continuously compounded mutual fund fee 3 structure (see Bernard et al (2014) and Shen et al (2016)) such that the resulting mutual fund value from the policyholder's perspective is…”

Section: Problem Statementmentioning

confidence: 99%

“…with γ t being the penalty percentage charged for surrendering at time t. As in Bernard et al (2014) and Shen et al (2016), we assume that γ t is exponentially decreasing with time and is equal to 1 − e −γ(T −t) implying that if the policyholder surrenders the guarantee at t ∈ [0, T ], equation 7becomes…”

Section: Problem Statementmentioning

confidence: 99%

“…As a way of discouraging policyholders from surrendering early, annuity providers normally charge penalty fees which takes a variety of functional forms. Bernard et al (2014) and Shen et al (2016) incorporate a penalty fee structure which is exponentially decreasing with time to maturity. Other penalty fee structures are discussed in Milevsky and Salisbury (2001) who denote such fees as deferred surrender charges.…”

Section: Introductionmentioning

confidence: 99%

“…Bacinello (2013) also values participating life insurance policies with surrender options using a recursive binomial tree approach. Shen et al (2016) take the annuity provider's perspective and use numerical quadrature techniques to derive expressions for fair management fees and the associated optimal surrender boundaries using the framework developed in Bernard et al (2014).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal surrender of guaranteed minimum maturity benefits under stochastic volatility and interest rates

Kang

Ziveyi

2018

Insurance: Mathematics and Economics

Self Cite

View full text Add to dashboard Cite

In this paper we analyse how the policyholder surrender behaviour is influenced by changes in various sources of risk impacting a variable annuity (VA) contract embedded with a guaranteed minimum maturity benefit rider that can be surrendered anytime prior to maturity. We model the underlying mutual fund dynamics by combining a Heston (1993) stochastic volatility model together with a Hull and White (1990) stochastic interest rate process. The model is able to capture the smile/skew often observed on equity option markets (Grzelak and Oosterlee, 2011) as well as the influence of the interest rates on the early surrender decisions as noted from our analysis. The annuity provider charges management fees which are proportional to the level of the mutual fund as a way of funding the VA contract. To determine the optimal surrender decisions, we present the problem as a 4-dimensional freeboundary partial differential equation (PDE) which is then solved efficiently by the method of lines (MOL) approach. The MOL algorithm facilitates simultaneous computation of the prices, fair management fees, optimal surrender boundaries and hedge ratios of the variable annuity contract as part of the solution at no additional computational cost. A comprehensive analysis on the impact of various risk factors in influencing the policyholder's surrender behaviour is carried out, highlighting the significance of both stochastic volatility and interest rate parameters in influencing the policyholder's surrender behaviour. With the aid of the hedge ratios obtained from the MOL, we construct an effective dynamic hedging strategy to mitigate the provider's risk and compare different hedging performances when the policyholders' surrender behaviour is either optimal or sub-optimal.

show abstract

Section: Problem Statementmentioning

confidence: 99%

Section: Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal surrender of guaranteed minimum maturity benefits under stochastic volatility and interest rates

Kang

Ziveyi

2018

Insurance: Mathematics and Economics

Self Cite

View full text Add to dashboard Cite

show abstract

“…ese guarantees embedded in VA contracts are similar to financial options. For instance, a guaranteed minimum accumulation benefit (GMAB) guarantees a lump sum amount at a predetermined future date, a guaranteed minimum death benefit (GMDB) guarantees a minimum lump sum upon death, a guaranteed minimum living benefit (GMLB) provides income guarantees to protect the policyholder's income from declining, and a guaranteed minimum maturity benefit (GMMB) is a guarantee that provides the policyholder with a minimum benefit on maturity of the VA contract (see the works of Bernard et al [1], Ignatieva et al [2], Bauer et al [3], and Shen et al [4]).…”

Section: Introductionmentioning

confidence: 99%

Optimal Surrender Policy of Guaranteed Minimum Maturity Benefits in Variable Annuities with Regime-Switching Volatility

Luo

Xing

2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This study investigates valuation of guaranteed minimum maturity benefits (GMMB) in variable annuity contract in the case where the guarantees can be surrendered at any time prior to the maturity. In the event of the option being exercised early, early surrender charges will be applied. We model the underlying mutual fund dynamics under regime-switching volatility. The valuation problem can be reduced to an American option pricing problem, which is essentially an optimal stopping problem. Then, we obtain the pricing partial differential equation by a standard Markovian argument. A detailed discussion shows that the solution of the problem involves an optimal surrender boundary. The properties of the optimal surrender boundary are given. The regime-switching Volterra-type integral equation of the optimal surrender boundary is derived by probabilistic methods. Furthermore, a sensitivity analysis is performed for the optimal surrender decision. In the end, we adopt the trinomial tree method to determine the optimal strategy.

show abstract

A variational inequality arising from optimal surrender of variable annuity with lookback benefit

Jeon

Kwak

2022

J Inequal Appl

View full text Add to dashboard Cite

We introduce a variable annuity (VA) contract with a surrender option and lookback benefit, that is, the benefit of the VA contract is linked to the maximum process of the policyholder’s account value. In contrast to the constant guarantee model provided in Bernard et al. (Insur. Math. Econ. 55:116–128, 2014), it is optimal for the policyholder of the VA contract with lookback benefit to surrender the VA contract when the policyholder’s account value is below or equal to the optimal surrender boundary. Thus, from the perspective of the insurer to construct a portfolio of VA contracts, utilizing the VA contracts with lookback benefit along with VA contracts with constant guarantee provides the diversification of early surrenders. The valuation of this contract can be described as a two-dimensional parabolic variational inequality. By converting this into the one-dimensional problem, we obtain the integral equations for the value function and the free boundary. The recursive integration method is applied to obtain the numerical solutions. We also provide comparative statics of the optimal surrender boundaries with respect to various parameters.

show abstract

Valuation of Guaranteed Minimum Maturity Benefits in Variable Annuities with Surrender Options

Cited by 3 publications

References 19 publications

Optimal surrender of guaranteed minimum maturity benefits under stochastic volatility and interest rates

Optimal surrender of guaranteed minimum maturity benefits under stochastic volatility and interest rates

Optimal Surrender Policy of Guaranteed Minimum Maturity Benefits in Variable Annuities with Regime-Switching Volatility

A variational inequality arising from optimal surrender of variable annuity with lookback benefit

Contact Info

Product

Resources

About