Title: On the pricing of single premium variable annuities with periodic fees and periodic cost of insurance using option pricing techniques

Authors: Thomas Poufinas

Addresses: Department of Statistics and Actuarial – Financial Mathematics, University of the Aegean, Karlovassi 83200, Samos, Greece

Abstract: The pricing of a series of products that combine insurance with investments, known as variable annuities, is considered. Given that there is a single premium instalment, then the death benefit at the time of death is equal to the maximum between the fund value and the sum assured. We have discussed in the past the problem in the case that there is a single premium instalment and the cost of insurance is collected at the beginning. We now move to examine the case that management fees need to be paid periodically via the cancellation of units and study the calculation of the charge that needs to be made by the insurer. We do not use standard actuarial techniques, but rather realise that the risk borne by the insurer resembles to the payoff of an option. We attempt to follow option valuation techniques in discrete time to find the insurance premium.

Keywords: single premium variable annuities; option pricing; binomial tree; probability of death; insurance costs; management fees; periodic fees; option valuation; insurance premiums.

DOI: 10.1504/IJFMD.2011.042599

International Journal of Financial Markets and Derivatives, 2011 Vol.2 No.3, pp.180 - 194

Published online: 18 Sep 2011 *

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