Exponential functionals of Lévy processes and variable annuity guaranteed benefits

Feng, Runhuan; Kuznetsov, Alexey; Yang, Fenghao

doi:10.1016/j.spa.2018.03.011

Cited by 10 publications

(4 citation statements)

References 26 publications

(31 reference statements)

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“…Under the Black-Scholes model assumptions, the dynamics of annuity account value are as follows [30]: where A t and c are denoted as the sub account value at time t and the mortality and expense fee payable continuously respectively. While k is the subsequent contributions to the sub-account [31].…”

Section: Methodsmentioning

confidence: 99%

An empirical study on asymmetric jump diffusion for option and annuity pricing

2019

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In this paper, we present a method to estimate the market parameters modelled by an asymmetric jump diffusion process. The method proposed is based on Kou’s jump diffusion model while the market parameters refer to the market drift, the market volatility, the jump intensity on market price, and the rate of jump occurrence in a consistent manner throughout the entire paper. The model captures the asymmetric nature of the price fluctuation during up trend markets and down trend markets. The results are compared to conventional options to observe the impact of jump effects. The results from simulation show that the asymmetric jump diffusion model can estimate the fair prices of European call options and annuity better than the Black-Scholes model and the symmetric jump diffusion model proposed by Kou and Merton.

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Section: Methodsmentioning

confidence: 99%

An empirical study on asymmetric jump diffusion for option and annuity pricing

2019

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“…For a broader perspective on the valuation of guaranteed benefit variable annuities, readers can refer to Feng and Jing (2017) [30], Feng and Yi (2019) [31], Liu (2021) [32], Moenig (2021) [33], and Gweon and Li (2023) [34] for additional insights and research outcomes.…”

Section: Related Literaturementioning

confidence: 99%

Valuation of a Mixture of GMIB and GMDB Variable Annuity

Han,

Li,

Fan

et al. 2024

Mathematics

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The Guaranteed Minimum Income Benefit (GMIB) and Guaranteed Minimum Death Benefit (GMDB) are options that may be included at the inception of a variable annuity (VA) contract. In exchange for small fees charged by the insurer, they give the policyholder a right to receive a guaranteed minimum level of annuity payment (GMIB) and a guaranteed minimum level of payment when the policyholder dies (GMDB), respectively. A combination of these two options may be attractive since it protects the policyholder’s investment from potential poor market behavior as well as mortality risk during the accumulation phase. This study examined the pricing of a composite variable annuity incorporating both the GMIB and GMDB options (a Guaranteed Minimum Income–Death Benefit, notated GMIDB). We used a non-arbitrage valuation method, decomposed the GMIDB value into two parts, and derived an analytical pricing formula based on a constant fee structure. The formula can be used to determine the fair fee to be charged. We conducted comprehensive sensitivity analyses on critical parameters to determine what drives the value of a GMIDB option. Our approach offers a simple and deterministic way to price a VA embedded with the GMIDB option. Our numerical findings suggested that the annuity conversion rate, age of the policyholder, and volatility of risky investments are significant in the valuation of a GMIDB option.

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“…where A t and c are denoted as the sub account value at time t and the mortality and expense fee payable continuously respectively. While k is the subsequent contributions to the subaccount [31].…”

Section: Pricing Annuity With Asymmetric Jump Diffusion Modelmentioning

confidence: 99%

An empirical study on asymmetric jump diffusion for option and annuity pricing

Joe

Kheng

Lai

2019

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH2018): Innovative Technologie

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In this paper, we present a method to estimate the market parameters modelled by an asymmetric jump diffusion process. The method proposed is based on Kou's jump diffusion model while the market parameters refer to the market drift, the market volatility, the jump intensity on market price, and the rate of jump occurrence in a consistent manner throughout the entire paper. The model captures the asymmetric nature of the price fluctuation during up trend markets and down trend markets. The results are compared to conventional options to observe the impact of jump effects. The results from simulation show that the asymmetric jump diffusion model can estimate the fair prices of European call options and annuity better than the Black-Scholes model and the symmetric jump diffusion model proposed by Kou and Merton.

show abstract

Exponential functionals of Lévy processes and variable annuity guaranteed benefits

Cited by 10 publications

References 26 publications

An empirical study on asymmetric jump diffusion for option and annuity pricing

An empirical study on asymmetric jump diffusion for option and annuity pricing

Valuation of a Mixture of GMIB and GMDB Variable Annuity

An empirical study on asymmetric jump diffusion for option and annuity pricing

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