Valuation of Hybrid Financial and Actuarial Products: A Universal 3-Step Method
32 Pages Posted: 9 Jan 2019
Date Written: December 27, 2018
Financial products are priced using risk-neutral expectations justified by hedging portfolios that (as accurate as possible) match the product's payoff. In insurance, premium calculations are based on a real-world best-estimate value plus a risk premium. The insurance risk premium is typically reduced by pooling of (in the best case) independent contracts. As hybrid life insurance contracts depend on both financial and insurance risks, their valuation requires a hybrid valuation principle that combines the two concepts of financial and actuarial valuation. The aim of this paper is to present a novel 3-step projection algorithm to valuate a class of hybrid contracts by decomposing their payoff in three parts: A financial, hedgeable part, a diversifiable actuarial part and a residual part that is neither hedgeable nor diversifiable. The method allows for a separate treatment of unsystematic, diversifiable mortality risk and systematic, aggregate mortality risk related to, for example, epidemics or population-wide improvements in life expectancy. We illustrate our method in the case of a pure endowment insurance contract with profit and compare the 3-step method to alternative premium principles suggested in the literature. We demonstrate that the 3-step method satisfies most of the desirable features of a premium principle and is straightforward to compute and implement.
Keywords: financial risk, actuarial valuation, (un)systematic mortality risk, contract valuation, risk decomposition, hedging
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