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Tree-based models for variable annuity valuation: parameter tuning and empirical analysis

Published online by Cambridge University Press:  16 March 2021

Zhiyu Quan ,
Guojun Gan  and
Emiliano Valdez
Zhiyu Quan
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Champaign, IL61801, USA
Guojun Gan*
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, CT06269-1009, USA
Emiliano Valdez
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, CT06269-1009, USA
*
*Corresponding author. E-mail: guojun.gan@uconn.edu
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Abstract

Variable annuities have become popular retirement and investment vehicles due to their attractive guarantee features. Nonetheless, managing the financial risks associated with the guarantees poses great challenges for insurers. One challenge is risk quantification, which involves frequent valuation of the guarantees. Insurers rely on the use of Monte Carlo simulation for valuation as the guarantees are too complicated to be valued by closed-form formulas. However, Monte Carlo simulation is computationally intensive. In this paper, we empirically explore the use of tree-based models for constructing metamodels for the valuation of the guarantees. In particular, we consider traditional regression trees, tree ensembles, and trees based on unbiased recursive partitioning. We compare the performance of tree-based models to that of existing models such as ordinary kriging and generalised beta of the second kind (GB2) regression. Our results show that tree-based models are efficient in producing accurate predictions and the gradient boosting method is considered the most superior in terms of prediction accuracy.

Keywords

Tree-based modelVariable annuityPortfolio valuationMetamodelling
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 16 , Issue 1 , March 2022 , pp. 95 - 118
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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