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EFFICIENT DYNAMIC HEDGING FOR LARGE VARIABLE ANNUITY PORTFOLIOS WITH MULTIPLE UNDERLYING ASSETS

Published online by Cambridge University Press:  11 August 2020

X. Sheldon Lin  and
Shuai Yang
X. Sheldon Lin
Affiliation:
Department of Statistical Sciences, University of Toronto, 100 St George Street, Toronto, ONM5S 3G3, Canada E-Mail: [email protected]
Shuai Yang*
Affiliation:
Department of Statistical Sciences, University of Toronto, 100 St George Street, Toronto, ONM5S 3G3, Canada E-Mail: [email protected] PathWise Solutions Group LLC Aon, Suite 2300, 20 Bay Street, Toronto, ONM5J 2N9, Canada E-Mails: [email protected], [email protected]
*
E-Mails: [email protected], [email protected]
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Abstract

A variable annuity (VA) is an equity-linked annuity that provides investment guarantees to its policyholder and its contributions are normally invested in multiple underlying assets (e.g., mutual funds), which exposes VA liability to significant market risks. Hedging the market risks is therefore crucial in risk managing a VA portfolio as the VA guarantees are long-dated liabilities that may span decades. In order to hedge the VA liability, the issuing insurance company would need to construct a hedging portfolio consisting of the underlying assets whose positions are often determined by the liability Greeks such as partial dollar Deltas. Usually, these quantities are calculated via nested simulation approach. For insurance companies that manage large VA portfolios (e.g., 100k+ policies), calculating those quantities is extremely time-consuming or even prohibitive due to the complexity of the guarantee payoffs and the stochastic-on-stochastic nature of the nested simulation algorithm. In this paper, we extend the surrogate model-assisted nest simulation approach in Lin and Yang [(2020) Insurance: Mathematics and Economics, 91, 85–103] to efficiently calculate the total VA liability and the partial dollar Deltas for large VA portfolios with multiple underlying assets. In our proposed algorithm, the nested simulation is run using small sets of selected representative policies and representative outer loops. As a result, the computing time is substantially reduced. The computational advantage of the proposed algorithm and the importance of dynamic hedging are further illustrated through a profit and loss (P&L) analysis for a large synthetic VA portfolio. Moreover, the robustness of the performance of the proposed algorithm is tested with multiple simulation runs. Numerical results show that the proposed algorithm is able to accurately approximate different quantities of interest and the performance is robust with respect to different sets of parameter inputs. Finally, we show how our approach could be extended to potentially incorporate stochastic interest rates and estimate other Greeks such as Rho.

Keywords

Variable annuity portfolionested simulationbalanced samplingspline regressiondynamic hedging
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 3 , September 2020 , pp. 913 - 957
Copyright
© 2020 by Astin Bulletin. All rights reserved

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