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Journal of Probability and Statistics
Volume 2010 (2010), Article ID 726389, 29 pages
Research Article

Pricing Equity-Indexed Annuities under Stochastic Interest Rates Using Copulas

Department of Mathematics and Statistics, Concordia University, Montreal, QC, Canada H3G 1M8

Received 1 October 2009; Accepted 18 February 2010

Academic Editor: Johanna Neslehova

Copyright © 2010 Patrice Gaillardetz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We develop a consistent evaluation approach for equity-linked insurance products under stochastic interest rates. This pricing approach requires that the premium information of standard insurance products is given exogenously. In order to evaluate equity-linked products, we derive three martingale probability measures that reproduce the information from standard insurance products, interest rates, and equity index. These risk adjusted martingale probability measures are determined using copula theory and evolve with the stochastic interest rate process. A detailed numerical analysis is performed for existing equity-indexed annuities in the North American market.