Valuation of hybrid financial and actuarial products in life insurance by a novel three-step method

Griselda Deelstra, Pierre Devolder (), Kossi Gnameho and Peter Hieber ()
Additional contact information
Griselda Deelstra: ULB
Pierre Devolder: Université catholique de Louvain, LIDAM/ISBA, Belgium
Kossi Gnameho: ULB
Peter Hieber: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2020020, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: 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 three-step projection algorithm to valuate 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 first two parts of the resulting premium are directly linked to their corresponding hedging and diversification strategies, respectively. 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 CAT bonds and a pure endowment insurance contract with profit and compare the three-step method to alternative valuation operators suggested in the literature.

Keywords: Keywords; Financial risk; actuarial valuation; contract valuation; incomplete markets; risk decomposition; hedging (search for similar items in EconPapers)
Date: 2020-03-01
Note: In: ASTIN Bulletin - Vol. 50, no.3, p. 709-742 (2020)
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Citations: View citations in EconPapers (14)

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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2020020

DOI: 10.1017/asb.2020.25

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