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The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case

Ballotta, L. and Haberman, S. (2006). The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case. Insurance: Mathematics and Economics, 38(1), pp. 195-214. doi: 10.1016/j.insmatheco.2005.10.002

Abstract

In this paper, we extend the analysis of the behaviour of pension contracts with guaranteed annuity conversion options (as presented in Ballotta and Haberman [Insurance: Math. Econ. 33 (2003) 87]) to the case in which mortality risk is incorporated via a stochastic model for the evolution over time of the underlying hazard rates. The pricing framework makes also use of a Black–Scholes/Heath–Jarrow–Morton economy in order to obtain an analytical solution to the fair valuation problem of the liabilities implied by these particular pension policies. The solution is not in closed form, and therefore, we resort to Monte Carlo simulation. Numerical results are investigated and the sensitivity of the price of the option to changes in the key parameters from the financial and mortality models is also analyzed.

Publication Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Insurance: Mathematics and Economics. Changes resulting from the publishing process, such as editing, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in INSURANCE: MATHEMATICS AND ECONOMICS, VOL38, ISSUE1, 24th February 2006, DOI:10.1016/j.insmatheco.2005.10.002
Publisher Keywords: Fair value; Guaranteed annuity options; Incomplete markets; Stochastic mortality
Subjects: H Social Sciences > HG Finance
Departments: Cass Business School > Actuarial Science & Insurance > Actuarial Research Reports
URI: http://openaccess.city.ac.uk/id/eprint/5815
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