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.
Highlights
A unit-linked insurance policy is a product offered by insurance companies
A minimum guaranteed amount that the insured will receive. The price of such contract depends on the age of the insured at the moment of entering the contract and the time of expiration, likewise, it depends on the event that the insured is alive at the time of expiration
The two basic elements needed in order to build a financial model robust enough to be able to price unit-linked policies are a financial market and a group of individuals to write insurance on
Summary
A unit-linked insurance policy is a product offered by insurance companies. Such contract specifies an event under which the insured of the contract obtains a fixed amount. Since there is more randomness in the model, complete hedging is no longer possible, the authors in Wang et al (2013) provide the so-called local risk minimizing strategies Another result that considers both stochastic interest rates and stochastic volatility is van Haastrecht et al (2009). There are available instruments in the market for hedging against volatility risk, the so-called forward variance swaps Such products are contracts on the future performance of the volatility of the stock. In such a way, we want to price unit-linked contracts taking into account that the insurance company can trade these instruments as well.
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