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A MIXED BOND AND EQUITY FUND MODEL FOR THE VALUATION OF VARIABLE ANNUITIES

Published online by Cambridge University Press:  04 November 2020

Maciej Augustyniak ,
Frédéric Godin  and
Emmanuel Hamel
Maciej Augustyniak
Affiliation:
Département de Mathématiques et de Statistique Université de Montréal Montreal (Quebec), Canada E-Mail: [email protected]
Frédéric Godin*
Affiliation:
Department of Mathematics and Statistics Concordia University Montreal (Quebec), Canada École d’Actuariat Université Laval Quebec (Quebec), Canada E-Mail: [email protected]
Emmanuel Hamel
Affiliation:
École d’Actuariat Université Laval Quebec (Quebec), Canada E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

Variable annuity (VA) policies are typically issued on mutual funds invested in both fixed income and equity asset classes. However, due to the lack of specialized models to represent the dynamics of fixed income fund returns, the literature has primarily focused on studying long-term investment guarantees on single-asset equity funds. This article develops a mixed bond and equity fund model in which the fund return is linked to movements of the yield curve. Theoretical motivation for our proposed specification is provided through an analogy with a portfolio of rolling horizon bonds. Moreover, basis risk between the portfolio return and its risk drivers is naturally incorporated into our framework. Numerical results show that the fit of our model to Canadian VA data is adequate. Finally, the valuation of VAs is illustrated and it is found that the prevailing interest rate environment can have a substantial impact on guarantee costs.

Keywords

Mutual fund modelbond fundyield curveinvestment guaranteevariable annuitiesbasis riskG32C51C63
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 1 , January 2021 , pp. 131 - 159
Copyright
© 2020 by Astin Bulletin. All rights reserved

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