The effect of management discretion on hedging and fair valuation of participating policies with maturity guarantees

Abstract

In this paper we consider how an insurer should invest in order to hedge the maturity guarantees inherent in participating policies. Many papers have considered the case where the guarantee is increased each year according to the performance of an exogenously given reference portfolio subject to some guaranteed rate. However, in this paper we will consider the more realistic case whereby the reference portfolio is replaced by the insurer’s own investments which are controlled completely at the discretion of the insurer’s management. Hence in our case any change in the insurer’s investment strategy leads to a change in the underlying value process of the participating contract. We use a binomial tree model to show how this risk can be hedged, and hence calculate the fair value of the contract at the outset.