The Role of the Dependence between Mortality and Interest Rates When Pricing Guaranteed Annuity Options

34 Pages Posted: 2 Oct 2015 Last revised: 12 Oct 2015

See all articles by Griselda Deelstra

Griselda Deelstra

Université Libre de Bruxelles (ULB)

Martino Grasselli

University of Padova - Department of Mathematics; Léonard de Vinci Pôle Universitaire, Research Center, Finance Group

Christopher Van Weverberg

Université Libre de Bruxelles (ULB)

Date Written: October 11, 2015

Abstract

In this paper we investigate the consequences on the pricing of insurance contingent claims when we relax the typical independence assumption made in the actuarial literature between mortality risk and interest rate risk. Starting from the Gaussian approach of Liu et al. (2014), we consider more general affine models where the mortality and interest rates remain positive and we derive pricing formulas for insurance contracts like Guaranteed Annuity Options (GAOs). In a Wishart affine model, which allows for a non-trivial dependence between the mortality and the interest rates, we go far beyond the results found in the Gaussian case by Liu et al. (2014), where the value of these insurance contracts can be explained only in terms of the initial pairwise linear correlation.

Keywords: Wishart process, Guaranteed Annuity Options, Stochastic mortality, Stochastic interest rates, Affine interest rate models, Dependence, Fourier

JEL Classification: C00

Suggested Citation

Deelstra, Griselda and Grasselli, Martino and Van Weverberg, Christopher, The Role of the Dependence between Mortality and Interest Rates When Pricing Guaranteed Annuity Options (October 11, 2015). Available at SSRN: https://ssrn.com/abstract=2667939 or http://dx.doi.org/10.2139/ssrn.2667939

Griselda Deelstra

Université Libre de Bruxelles (ULB) ( email )

Boulevard du Triomphe, CP210
Brussels, Brussels 1050
Belgium

Martino Grasselli

University of Padova - Department of Mathematics ( email )

Via Trieste 63
Padova, Padova
Italy

Léonard de Vinci Pôle Universitaire, Research Center, Finance Group ( email )

Paris La Défense
France

Christopher Van Weverberg (Contact Author)

Université Libre de Bruxelles (ULB) ( email )

CP210, boulevard du Triomphe
Brussels, Brussels 1050
Belgium

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