Efficient hedging for equity-linked life insurance contracts with stochastic interest rate

Abstract

This paper studies the problem of valuation equity-linked life insurance contracts with efficient hedging technique in a stochastic interest environment. In our setting, the payoff of such contracts is based on two risky assets governed by the Black–Scholes models: one is responsible for future gains, the other one is a stochastic guarantee. The behaviour of the stochastic interest rate is described by the Heath–Jarrow–Morton model. Explicit formulas for both the price of a single premium contract and the survival probability were derived respectively. A numerical example illustrates how a risk-taking insurance company may apply this efficient hedging technique to manage the balance between financial and insurance risks.