Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-23T22:36:08.892Z Has data issue: false hasContentIssue false
  • English
  • Français

A Natural Hedge for Equity Indexed Annuities

Published online by Cambridge University Press:  08 June 2011

Carole Bernard  and
Phelim P. Boyle
Get access Rights & Permissions [Opens in a new window]

Abstract

Equity linked products are popular in many countries. These contracts generally provide a guaranteed return combined with some participation in the market performance, often computed using a complicated formula. Hedging these contracts often presents a real challenge for insurers in particular during a financial crisis. In this paper, we explain how insurers can benefit from selling a pool of different contracts with different sensitivities to certain key variables to reduce risk exposure. We show how they can diversify their menu of policy designs to stabilize the market value of their liabilities against changes in the market volatility and against estimation error in the volatility parameter. We illustrate the methodology with specific examples of equity annuity contracts with opposite sensitivities to vega risk.

Keywords

Natural hedgingParticipating policiesAnnual guaranteeCliquet optionMaturity guaranteeSolvency IIIFRSLocal capMarket valuation
Type
Papers
Information
Annals of Actuarial Science , Volume 5 , Issue 2 , September 2011 , pp. 211 - 230
Copyright
Copyright © Institute and Faculty of Actuaries 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bacinello, A.R. (2001). Fair Pricing of Life Insurance Participating Policies With a Minimum Interest Rate Guaranteed. Astin Bulletin, 31(2), 275–297.Google Scholar
Bacinello, A.R. (2003a). Fair Valuation of a Guaranteed Life Insurance Participating Contract Embedding a Surrender Option. The Journal of Risk and Insurance, 70(3), 461–487.Google Scholar
Bacinello, A.R. (2003b). Pricing Guaranteed Life Insurance Participating Policies With Annual Premiums and Surrender Option. North American Actuarial Journal, 7(3), 1–17.CrossRefGoogle Scholar
Bacinello, A.R. (2005). Endogenous Model of Surrender Conditions in Equity-Linked Life Insurance. Insurance: Mathematics and Economics, 37(2), 270–296.Google Scholar
Ballotta, L. (2005). A Lévy Process-Based Framework for the Fair Valuation of Participating Life Insurance Contracts. Special Issue of Insurance: Mathematics and Economics, 37(2), 173–196.Google Scholar
Ballotta, L., Haberman, S., Wang, N. (2005). Guarantees in With-Profit and Unitised With-Profit Life Insurance Contracts: Fair Valuation Problem in Presence of the Default Option. Journal of Risk and Insurance, 73(1), 97–121.CrossRefGoogle Scholar
Barbarin, J., Devolder, P. (2005). Risk measure and fair valuation of an investment guarantee in life insurance. Insurance: Mathematics and Economics, 37(2), 297–323.Google Scholar
Bernard, C., Lemieux, C. (2008). Fast Simulation on Equity-linked Life Insurance Contracts with a Surrender Option. Proceedings of the 2008 Winter Simulation Conference.CrossRefGoogle Scholar
Bernard, C., Le Courtois, O., Quittard-Pinon, F. (2005). Market Value of Life Insurance Contracts under Stochastic Interest Rates and Default Risk. Insurance: Mathematics and Economics, 36(3), 499–516.Google Scholar
Bernard, C., Le Courtois, O., Quittard-Pinon, F. (2006). Development and Pricing of a New Participating Contract. North American Actuarial Journal, 10(4), 179–195.Google Scholar
Bernard, C., Boyle, P.P., Gornall, W. (2011). Locally-Capped Investment Products and the Retail Investor. Journal of Derivatives, 18(4), 72–88.CrossRefGoogle Scholar
Blanchard, R. (2008). When is U.S. GAAP Going Away? Actuarial Review, 35(3), 9.Google Scholar
Boyle, P.P., Hardy, M.R. (1997). Reserving for Maturity Guarantees: Two Approaches. Insurance: Mathematics and Economics, 21(2), 113–127.Google Scholar
Boyle, P.P., Hardy, M.R. (2003). Guaranteed Annuity Options. Astin Bulletin, 33(2), 125–152.Google Scholar
Boyle, P.P., Schwartz, E.S. (1977). Equilibrium Prices of Guarantees under Equity-Linked Contracts. Journal of Risk and Insurance, 44, 639–660.Google Scholar
Brennan, M.J., Schwartz, E.S. (1976). The Pricing of Equity-linked Life Insurance Policies with an Asset Value Guarantee. Journal of Financial Economics, 3, 195–213.Google Scholar
Carr, P., Madan, D.B. (1999). Option Pricing and the Fast Fourier Transform. Journal of Computational Finance, 1, 61–73.CrossRefGoogle Scholar
Gatzert, N., Schmeiser, H. (2006). Implicit Options in Life Insurance: Valuation and Risk Management. Zeitschrift fr die gesamte Versicherungswissenschaft, 95(4), 111–128.CrossRefGoogle Scholar
Grosen, A., Jørgensen, P.L. (1997). Valuation of Early Exercisable Interest Rate Guarantees. Journal of Risk and Insurance, 64(3), 481–503.Google Scholar
Grosen, A., Jørgensen, P.L. (2000). Fair Valuation of Life Insurance Liabilities: The Impact of Interest Rate Guarantees, Surrender Options, and Bonus Policies. Insurance: Mathematics and Economics, 26(1), 37–57.Google Scholar
Grosen, A., Jørgensen, P.L. (2002). Life Insurance Liabilities at Market Value: An Analysis of Insolvency Risk, Bonus Policy, and Regulatory Intervention Rules in a Barrier Option Framework. Journal of Risk and Insurance, 69(1), 63–91.Google Scholar
Hansen, F. (2004). Get Ready for New Global Accounting Standards. Business Finance.Google Scholar
Hardy, M.R. (2003). Investment Guarantees: Modelling and Risk Management for Equity-Linked Life Insurance. Wiley.Google Scholar
Hull, J. (2003). Options, Futures and Other Derivatives. 5 edn. Pearson Education.Google Scholar
Jørgensen, P.L. (2004). On Accounting Standards and Fair Valuation of Life Insurance and Pension Liabilities. Scandinavian Actuarial Journal, 5, 372–394.CrossRefGoogle Scholar
Koco, L. (2007). Annuity Sales Slid 7% in 2006. National Underwriter Life and Health, 111(13), 8–9.Google Scholar
Lin, Y., Cox, S. (2007). Natural Hedging of Life and Annuity Mortality Risks. North American Actuarial Journal, 11(3), 1–15.Google Scholar
Miltersen, K.R., Persson, S.A. (2003). Guaranteed Investment Contracts: Distributed and Undistributed Excess Return. Scandinavian Actuarial Journal, 4, 257–279.CrossRefGoogle Scholar
Nielsen, J.A., Sandmann, K. (1995). Equity-linked Life Insurance: a model with stochastic interest rates. Insurance: Mathematics and Economics, 16(3), 225–253.Google Scholar
Palmer, B.A. (2006). Equity-Indexed Annuities: Fundamental Concepts and Issues. Working Paper, Information Insurance Institute, server.iii.org/yy_obj_data/binary/773405_1_0/EIA_paper.pdf.Google Scholar
Piggott, J., Valdez, E.A., Detzel, B. (2005). The Simple Analytics of a Pooled Annuity Fund. Journal of Risk and Insurance, 72(3), 497–520.Google Scholar
Plantin, G., Sapra, H., Shin, H.S. (2004). Fair Value Reporting Standards and Market Volatility. Derivatives Accounting and Risk Management: Key Concepts and the Impact of IAS 39, Risk Books.Google Scholar
SEC/NASD. (2004). On Examination Findings Regarding Broker-Dealer Sales Of Variable Insurance Products. Technical report - Joint Report.Google Scholar
Sun, P., Mungan, K., Corrigan, J., Finkelstein, G. (2009). Performance of insurance company hedging programs during the recent capital market crisis. Milliman Research Report, http://www.milliman.com/expertise/life-financial/publications/rr/pdfs/performance-insurance-company-hedging-rr12-01-08.pdf.Google Scholar
Tanskanen, A.J., Lukkarinen, J. (2003). Fair Valuation of Path-dependent Participating Life Insurance Contracts. Insurance: Mathematics and Economics, 33(3), 595–609.Google Scholar
Wilmott, P. (2002). Cliquet Options and Volatility Models. Wilmott Magazine, 1, 78–83.CrossRefGoogle Scholar