Variance and Interest Rate Risk in Unit-Linked Insurance Policies

Abstract

One of the risks derived from selling long-term policies that any insurance company has arises from interest rates. In this paper, we consider a general class of stochastic volatility models written in forward variance form. We also deal with stochastic interest rates to obtain the risk-free price for unit-linked life insurance contracts, as well as providing a perfect hedging strategy by completing the market. We conclude with a simulation experiment, where we price unit-linked policies using Norwegian mortality rates. In addition, we compare prices for the classical Black-Scholes model against the Heston stochastic volatility model with a Vasicek interest rate model.

Life insurance policies with cash flows subject to random interest rate changes

“…We mention [1,2] for some specific interest rate models and [3,7,9] for more general models in the framework of Heath-Jarrow-Morton. A model for the interest rate of diffusion type was considered by Norberg and Møller in [10] and by the authors in [4] where they look at unit-linked insurances with variance risk, as well.…”