Variance and interest rate risk in unit-linked insurance policies

TL;DR

This paper models interest rate and volatility risks in long-term insurance policies using advanced stochastic models, providing pricing and hedging strategies, and compares different financial models through simulations.

Contribution

It introduces a comprehensive framework combining stochastic volatility and interest rate models for pricing and hedging unit-linked insurance policies.

Findings

Heston model with Vasicek interest rates affects policy pricing.

Market completion allows perfect hedging of interest rate risk.

Simulation with Norwegian data demonstrates model applicability.

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.