Pricing guaranteed minimum withdrawal benefits under stochastic interest rates

Peng, Jingjiang; Leung, Kwai Sun; Kwok, Yue Kuen

doi:10.1080/14697680903436606

Cited by 60 publications

(18 citation statements)

References 8 publications

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“…We graphically interpret results presented inPeng et al (2012) to indicate that the total value of the put option varies by approximately 0.5% of the guarantee amount for a 0.1 variation in the correlation coefficient, given reasonable values for other parameters.…”

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confidence: 68%

A Survey of Valuation Issues for Hybrid Retirement Income Scheme Products

Evans

2016

SSRN Journal

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So-called variable annuity products which provide certain guaranteed minimum benefits are popular in the United States and Europe but are only in their infancy in Australia. We consider hybrid products with minimum withdrawal rates guaranteed for a fixed term or for life and the financial derivatives embedded in them. A capital markets style model can be used to value the product issuer's liability under the contract and measure their exposure to equity prices, interest rates, volatility and mortality risk. We survey recent literature for analysis of the valuation challenge faced by product issuers. We find that the guarantees generate material exposure for the issuers and that model based valuation can be informative for a dynamic hedging strategy or to derive risk sensitive measures of required capital and reserves.

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confidence: 68%

A Survey of Valuation Issues for Hybrid Retirement Income Scheme Products

Evans

2016

SSRN Journal

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“…Since the price of the VA, V, at time 0 is set equal to the guarantee account, the insurer funds the GMWB by charging a proportional fee, α, on the sub-account W, which is invested into a risky fund, F. Significant amount of research on pricing GMWBs has focused on finding this fair proportional fee (see Milevsky and Salisbury, 2006, Peng et al, 2012. Furthermore, argue that the fee charged can be split into two components, namely, a portion paid for the provision of the guarantee, α g , and the mutual fund management fee, α m , such that…”

Section: Valuation Of Gmwb Without Mortalitymentioning

confidence: 99%

Fourier Space Time-Stepping Algorithm for Valuing Guaranteed Minimum Withdrawal Benefits in Variable Annuities Under Regime-Switching and Stochastic Mortality

Ignatieva¹,

Song²,

Ziveyi³

2017

ASTIN Bull.

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This paper introduces the Fourier Space Time-Stepping algorithm to the valuation of variable annuity (VA) contracts embedded with guaranteed minimum withdrawal benefit (GMWB) riders when the underlying fund dynamics evolve under the influence of a regime-switching model. Mortality risk is introduced to the valuation framework by incorporating a two-factor affine stochastic mortality model proposed in Blackburn and Sherris (2013). The paper considers both, static and dynamic policyholder withdrawal behaviour associated with GMWB riders and assesses how model parameters influence the fees levied on providing such guarantees. Our numerical experiments reveal that the GMWB fees are very sensitive to regime-switching parameters; a percentage increase in the force of interest results in significant decrease in guarantee fees. The guarantee fees increase substantially with increasing volatility levels. Numerical experiments also highlight an increasing importance of mortality as maturity of the VA contract increases. Mortality has less impact on shorter maturity contracts regardless of the policyholder's withdrawal behaviour. As much as mortality influences pricing results for long maturities, the associated guarantee fees are decreasing functions of maturities for the VA contracts. Robustness checks of the Fourier Space Time-Stepping algorithm are performed by making numerical comparisons with several existing valuation approaches.

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“…Several authors have investigated the possibility of evaluating GMWB contracts while considering a stochastic interest rate. For example, Peng et al (2012) develop an analytic approximation of the fair value of the GMWB under the Vasicek stochastic interest rate model. Donnelly et al (2014) consider pricing and Greeks calculation through an Alternating Direction Implicit method in the advanced Heston-Hull-White model.…”

Section: Introductionmentioning

confidence: 99%

Taxation of a GMWB Variable Annuity in a Stochastic Interest Rate Model

Molent

2020

ASTIN Bull.

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Modeling taxation of Variable Annuities has been frequently neglected, but accounting for it can significantly improve the explanation of the withdrawal dynamics and lead to a better modeling of the financial cost of these insurance products. The importance of including a model for taxation has first been observed by Moenig and Bauer (2016) while considering a Guaranteed Minimum Withdrawal Benefit (GMWB) Variable Annuity. In particular, they consider the simple Black–Scholes dynamics to describe the underlying security. Nevertheless, GMWB are long-term products, and thus accounting for stochastic interest rate has relevant effects on both the financial evaluation and the policyholder behavior, as observed by Goudenège et al. (2018). In this paper, we investigate the outcomes of these two elements together on GMWB evaluation. To this aim, we develop a numerical framework which allows one to efficiently compute the fair value of a policy. Numerical results show that accounting for both taxation and stochastic interest rate has a determinant impact on the withdrawal strategy and on the cost of GMWB contracts. In addition, it can explain why these products are so popular with people looking for a protected form of investment for retirement.

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Pricing guaranteed minimum withdrawal benefits under stochastic interest rates

Cited by 60 publications

References 8 publications

A Survey of Valuation Issues for Hybrid Retirement Income Scheme Products

A Survey of Valuation Issues for Hybrid Retirement Income Scheme Products

Fourier Space Time-Stepping Algorithm for Valuing Guaranteed Minimum Withdrawal Benefits in Variable Annuities Under Regime-Switching and Stochastic Mortality

Taxation of a GMWB Variable Annuity in a Stochastic Interest Rate Model

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