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Efficient Greek Calculation of Variable Annuity Portfolios for Dynamic Hedging: A Two-Level Metamodeling Approach

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  • Guojun Gan
  • X. Sheldon Lin

Abstract

The financial risk associated with the guarantees embedded in variable annuities cannot be addressed adequately by traditional actuarial techniques. Dynamical hedging is used in practice to mitigate the financial risk arising from variable annuities. However, a major challenge of dynamical hedging is to calculate the dollar Deltas of a portfolio of variable annuities within a short time interval so that rebalancing can be done on a timely basis. In this article, we propose a two-level metamodeling approach to efficiently estimating the partial dollar Deltas of a portfolio of variable annuities under a multiasset framework. The first-level metamodel is used to estimate the partial dollar Deltas at some well-chosen market levels, and the second-level metamodel is used to estimate the partial dollar Deltas at the current market level based on the precalculated partial dollar Deltas. Our numerical results show that the proposed approach performs well in terms of accuracy and speed.

Suggested Citation

  • Guojun Gan & X. Sheldon Lin, 2017. "Efficient Greek Calculation of Variable Annuity Portfolios for Dynamic Hedging: A Two-Level Metamodeling Approach," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(2), pages 161-177, April.
    • Handle: RePEc:taf:uaajxx:v:21:y:2017:i:2:p:161-177
    DOI: 10.1080/10920277.2016.1245623
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    Cited by:

    1. Guojun Gan & Emiliano A. Valdez, 2018. "Nested Stochastic Valuation of Large Variable Annuity Portfolios: Monte Carlo Simulation and Synthetic Datasets," Data, MDPI, vol. 3(3), pages 1-21, September.
    2. Ludovic Goudenège & Andrea Molent & Antonino Zanette, 2021. "Gaussian process regression for pricing variable annuities with stochastic volatility and interest rate," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 57-72, June.
    3. Guojun Gan, 2018. "Valuation of Large Variable Annuity Portfolios Using Linear Models with Interactions," Risks, MDPI, vol. 6(3), pages 1-19, July.
    4. Jiang, Ruihong & Saunders, David & Weng, Chengguo, 2023. "Two-phase selection of representative contracts for valuation of large variable annuity portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 293-309.
    5. Tak Kuen Siu & Robert J. Elliott, 2019. "Hedging Options In A Doubly Markov-Modulated Financial Market Via Stochastic Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-41, December.
    6. Nguyen, Hang & Sherris, Michael & Villegas, Andrés M. & Ziveyi, Jonathan, 2024. "Scenario selection with LASSO regression for the valuation of variable annuity portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 27-43.
    7. Daniel Doyle & Chris Groendyke, 2018. "Using Neural Networks to Price and Hedge Variable Annuity Guarantees," Risks, MDPI, vol. 7(1), pages 1-19, December.
    8. Wing Fung Chong & Haoen Cui & Yuxuan Li, 2021. "Pseudo-Model-Free Hedging for Variable Annuities via Deep Reinforcement Learning," Papers 2107.03340, arXiv.org, revised Oct 2022.
    9. Thorsten Moenig, 2021. "Efficient valuation of variable annuity portfolios with dynamic programming," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(4), pages 1023-1055, December.
    10. Runhuan Feng & Peng Li, 2021. "Sample Recycling Method -- A New Approach to Efficient Nested Monte Carlo Simulations," Papers 2106.06028, arXiv.org.

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