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Equity-linked products: evaluation of the dynamic hedging errors under stochastic mortality

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Abstract

In this paper, we analyze the effect of unpredicted changes in mortality rates on the risk incurred by the sale of equity-indexed annuities (EIAs). Jumps in mortality indices due to catastrophes (for example, the 1918 flu pandemic) may occur in the future, causing important financial losses to insurers selling products offering death benefits. Thus, we analyze the distribution of hedging errors extracted from the dynamic hedging strategy underlying the fair valuation. To model mortality jumps stochastically, we use a regime-switching model introduced by Milidonis et al. (North Am Actuarial J 15(2):266–289, 2011). We then employ Esscher transforms to obtain closed-form expressions for the price of a term-end EIA at any time between the inception of the contract and its maturity date. The hedging strategy is derived from that valuation, and hedging errors are extracted from this strategy since it is not self-financing. A detailed numerical analysis is performed for a term-end EIA.

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Notes

  1. On the one hand the financial tracking errors are decreasing as the number of trading dates increases. On the other hand, fewer trading dates may lead to less expensive replicating portfolios when including transaction costs.

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Acknowledgments

This research was supported by the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

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

    Patrice Gaillardetz

  2. The Economical Insurance Group, Waterloo, ON, N2J 4S4, Canada

    Huan Yi Li

  3. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Anne MacKay

Authors
  1. Patrice Gaillardetz
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  2. Huan Yi Li
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  3. Anne MacKay
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Correspondence to Patrice Gaillardetz.

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Gaillardetz, P., Li, H.Y. & MacKay, A. Equity-linked products: evaluation of the dynamic hedging errors under stochastic mortality. Eur. Actuar. J. 2, 243–258 (2012). https://doi.org/10.1007/s13385-012-0057-1

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  • DOI: https://doi.org/10.1007/s13385-012-0057-1

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