Valuation of Hybrid Financial and Actuarial Products: A Universal 3-Step Method

32 Pages Posted: 9 Jan 2019

See all articles by Griselda Deelstra

Griselda Deelstra

Université Libre de Bruxelles (ULB)

Pierre Devolder

Catholic University of Louvain

Kossi Gnameho

Maastricht University - Department of Quantitative Economics

Peter Hieber

University of Ulm - Department of Mathematics and Economics; Technische Universität München (TUM) - Department of Mathematics

Date Written: December 27, 2018

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 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

Suggested Citation

Deelstra, Griselda and Devolder, Pierre and Gnameho, Kossi and Hieber, Peter, Valuation of Hybrid Financial and Actuarial Products: A Universal 3-Step Method (December 27, 2018). Available at SSRN: https://ssrn.com/abstract=3307061 or http://dx.doi.org/10.2139/ssrn.3307061

Griselda Deelstra

Université Libre de Bruxelles (ULB) ( email )

Boulevard du Triomphe, CP210
Brussels, Brussels 1050
Belgium

Pierre Devolder

Catholic University of Louvain ( email )

Place Montesquieu, 3
B-1348 Louvain-la-Neuve, 1348
Belgium

Kossi Gnameho

Maastricht University - Department of Quantitative Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

Peter Hieber (Contact Author)

University of Ulm - Department of Mathematics and Economics ( email )

Helmholzstrasse
Ulm, D-89081
Germany

Technische Universität München (TUM) - Department of Mathematics ( email )

Boltzmannstr. 3
Garching bei München, Bavaria 85748
Germany

Register to save articles to
your library

Register

Paper statistics

Downloads
27
Abstract Views
161
PlumX Metrics