A Time Series Framework for Pricing Guaranteed Lifelong Withdrawal Benefit

Sharma, Nitu; Selvamuthu, Dharmaraja; Arunachalam, Viswanathan

doi:10.1007/s10614-020-09999-9

Cited by 4 publications

(8 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One of the generalizations will be to consider stochastic mortality. The volatility clustering phenomenon is repeatedly observed in markets, therefore, appending a stochastic volatility model as proposed by Sharma et al 8 will capture such phenomenon. Another future research problem could be the calibration of parameters for JDMFBM models.…”

Section: Discussionmentioning

confidence: 99%

“…Some of the popular variations of the GBM model involve consideration of jumps (denoted by jump‐diffusion Brownian motion (JDBM) models), stochastic volatility, stochastic interest rate, and correlated jump‐diffusion processes. Some of the recent literature in VA pricing using variants of GBM model includes articles by Ballotta et al, 3 Gerber et al, 4 Ko and Bae, 5 Escobar et al, 6 Yu et al, 7 Sharma et al, 8 and Sharma et al 9 . Gerber et al 4 valued the GMDB rider using a JDBM model.…”

Section: Introductionmentioning

confidence: 99%

“…They used the Gompertz–Makeham model for mortality modeling by assuming independence between investment and demographic risk. Sharma et al 8 priced a GLWB rider using a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. The correlated jump‐diffusion model is used for modeling investment risk in an equity‐indexed annuities (EIAs) contract by Sharma et al 9 .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Variable annuities valuation under a mixed fractional Brownian motion environment with jumps considering mortality risk

Sharma

Selvamuthu

Natarajan

2022

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

Pricing a variable annuity (VA) is traditionally based on models with standard Brownian motion (BM). The assumption of independent increments in the BM is not always realistic as the price process of the risky assets exhibit a long-range dependency. To model such assets, a fractional Brownian motion (FBM) with Hurst parameter)is an appropriate model. However, due to arbitrage in an FBM model and jumps in stock returns, we consider in this work a mixed FBM (MFBM) model with jumps and evaluate variable annuities with different riders. We analyze the proposed model numerically to see the impact of mortality risk. We perform a comparison between eight stochastic models to obtain the best-suited mortality model, for a dataset of the US male population. Finally, we obtain the price of VA guarantees using the forecasted values from the fitted mortality model.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Variable annuities valuation under a mixed fractional Brownian motion environment with jumps considering mortality risk

Sharma

Selvamuthu

Natarajan

2022

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recently Sharma et al 7 developed a time‐series framework to obtain a fair price for the variable annuity embedded with GLWB. To overcome the limitations of the GBM model, they proposed a time series model for pricing an annuity using GARCH models.…”

Section: Introductionmentioning

confidence: 99%

“…In the work of Sharma et al, 7 sensitivity analysis has been performed between the GLWB fund and the varying risk‐free rate, resulting in significant variations in the fund value with a slight variation in the rate of interest. In this direction, Claymore Marshall et al 8 had shown that the GMIB value changes significantly with a slight change in interest rate.…”

Section: Introductionmentioning

confidence: 99%

Time series model for GLWB with surrender benefit and stochastic interest rate: Dynamic withdrawal approach

Singh

Arunachalam

Selvamuthu

2023

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

This study investigates the pricing problem of a variable annuity (VA) contract embedded with a guaranteed lifetime withdrawal benefit (GLWB) rider. VAs are annuities in which the value is linked to a bond and equity sub‐account fund. The guaranteed lifetime withdrawal benefit rider regularly provides a series of payments to the policyholder for the term of the policy while he/she is alive, regardless of portfolio performance. At the time of the policyholder's death, the remaining fund value is given to his nominee. Therefore, proper fund modeling is critical in the pricing of VA products. Several writers in the literature used a GBM model in which variance is considered to be constant to represent the fund value in a variable annuity contract. However, on the other hand, the returns on financial assets are non‐normally distributed in real life. A bit much Kurtosis, leverage effect, and Non‐zero Skewness characterize the returns. The generalized autoregressive conditional heteroscedastic (GARCH) models are also used for presenting a discrete framework for the pricing of GLWB. Still, the interest rate was kept constant without including the surrender benefit and the static withdrawal approach, which keeps the model far from the real scenario. Thus, in this research, the generalized GARCH models are used with surrender benefit and dynamic withdrawal strategy to develop a time series model for the pricing of annuity that overcomes the constraints of previous models. A numerical illustration and sensitivity analysis are used to examine the suggested model.

show abstract