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LESS-EXPENSIVE VALUATION AND RESERVING OF LONG-DATED VARIABLE ANNUITIES WHEN INTEREST RATES AND MORTALITY RATES ARE STOCHASTIC

Published online by Cambridge University Press:  13 April 2020

Kevin Fergusson Open the ORCID record for Kevin Fergusson [Opens in a new window]
Kevin Fergusson*
Affiliation:
University of Melbourne Victoria3010, Australia
*
E-Mail: kevin.fergusson@unimelb.edu.au
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Abstract

Variable annuities are products offered by pension funds and life offices that provide periodic future payments to the investor and often have ancillary benefits that guarantee survival benefits or sums insured on death. This paper extends the benchmark approach to value and hedge long-dated variable annuities using a combination of cash, bonds and equities under a variety of market models, allowing for dependence between financial and insurance markets. Under a simplified case of independence, the results show that when the discounted index is modelled as a time-transformed squared Bessel process, less-expensive valuation and reserving is achieved regardless of the short rate model or the mortality model.

Keywords

Variable annuitiesgrowth optimal portfoliobenchmark approachlong-dated equity index optionsminimal market modelstochastic short ratestochastic mortality ratesG10G13
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 2 , May 2020 , pp. 381 - 417
Copyright
© Astin Bulletin 2020

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