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A Time Series Framework for Pricing Guaranteed Lifelong Withdrawal Benefit

Author

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  • Nitu Sharma

    (Indian Institute of Technology Delhi)

  • S. Dharmaraja

    (Indian Institute of Technology Delhi)

  • Viswanathan Arunachalam

    (Universidad Nacional de Colombia)

Abstract

In this work, the pricing problem of a variable annuity (VA) contract embedded with a guaranteed lifelong withdrawal benefit (GLWB) rider has been considered. VAs are annuities whose value is linked with a sub-account fund consisting of bonds and equities. The GLWB rider provides a series of regular payments to the policyholder during the policy duration when he is alive irrespective of the portfolio performance. Also, the remaining fund value is given to his nominee, at the time of death of the policyholder. The appropriate modelling of fund plays a crucial role in the pricing of VA products. In the literature, several authors model the fund value in a VA contract using a geometric Brownian motion (GBM) model with a constant variance. However, in real life, the financial assets returns are not Normal distributed. The returns have non-zero skewness, high kurtosis, and leverage effect. This paper proposes a discrete-time model for annuity pricing using generalized autoregressive conditional heteroscedastic (GARCH) models, which overcome the limitations of the GBM model. The proposed model is analyzed with numerical illustration along with sensitivity analysis.

Suggested Citation

  • Nitu Sharma & S. Dharmaraja & Viswanathan Arunachalam, 2021. "A Time Series Framework for Pricing Guaranteed Lifelong Withdrawal Benefit," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 1225-1261, December.
    • Handle: RePEc:kap:compec:v:58:y:2021:i:4:d:10.1007_s10614-020-09999-9
    DOI: 10.1007/s10614-020-09999-9
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