On the pricing of regular premium variable annuities using options

Abstract

We consider the pricing of products that combine insurance with investments, known as variable annuities. We have visited in the past the problem when the premium is paid with a single instalment and the cost of insurance is collected either at the beginning of the policy or periodically. We move to examine the case of periodic premium payment so as to investigate the calculation of the cost 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 regular premium. We face the problem without and with management fees. In addition, we price when two more product features that we have excluded from our previous approach are offered; the payment of top ups and the possibility to surrender, before the policy maturity.