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RISK-BASED CAPITAL FOR VARIABLE ANNUITY UNDER STOCHASTIC INTEREST RATE

Published online by Cambridge University Press:  25 June 2020

JinDong Wang  and
Wei Xu
JinDong Wang
Affiliation:
School of Mathematical Sciences, Peking University, Beijing, China, E-Mail: jdwang@pku.edu.cn
Wei Xu*
Affiliation:
Department of Mathematics, Ryerson University, Toronto, ON, Canada, E-Mail: wei.xu@ryerson.ca
*
E-Mail: wei.xu@ryerson.ca
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Abstract

Interest rate is one of the main risks for the liability of the variable annuity (VA) due to its long maturity. However, most existing studies on the risk measures of the VA assume a constant interest rate. In this paper, we propose an efficient two-dimensional willow tree method to compute the liability distribution of the VA with the joint dynamics of the mutual fund and interest rate. The risk measures can then be computed by the backward induction on the tree structure. We also analyze the sensitivity and impact on the risk measures with regard to the market model parameters, contract attributes, and monetary policy changes. It illustrates that the liability of the VA is determined by the long-term interest rate whose increment leads to a decrease in the liability. The positive correlation between the interest rate and mutual fund generates a fat-tailed liability distribution. Moreover, the monetary policy change has a bigger impact on the long-term VAs than the short-term contracts.

Keywords

Variable annuityvalue at riskconditional tail expectationGMWBGMDBGMMBtwo-factor willow tree methodstochastic interest rateHull–White model
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 3 , September 2020 , pp. 959 - 999
Copyright
© 2020 by Astin Bulletin. All rights reserved

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Footnotes

*

This work is supported by National Natural Science Fund of China (No. U1811462) and the Natural Sciences and Engineering Research Council of Canada (RGPIN-2020-04686).

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