Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T08:28:52.841Z Has data issue: false hasContentIssue false
  • English
  • Français

Guaranteed Annuity Options

Published online by Cambridge University Press:  17 April 2015

Phelim Boyle  and
Mary Hardy
Phelim Boyle
Affiliation:
Centre for Advanced Studies in Finance, School of Accountancy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Mary Hardy
Affiliation:
Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario Canada N2L 3G1
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Under a guaranteed annuity option, an insurer guarantees to convert a policyholder's accumulated funds to a life annuity at a fixed rate when the policy matures. If the annuity rates provided under the guarantee are more beneficial to the policyholder than the prevailing rates in the market the insurer has to make up the difference. Such guarantees are common in many US tax sheltered insurance products. These guarantees were popular in UK retirement savings contracts issued in the 1970's and 1980's when long-term interest rates were high. At that time, the options were very far out of the money and insurance companies apparently assumed that interest rates would remain high and thus that the guarantees would never become active. In the 1990's, as long-term interest rates began to fall, the value of these guarantees rose. Because of the way the guarantee was written, two other factors influenced the cost of these guarantees. First, strong stock market performance meant that the amounts to which the guarantee applied increased significantly. Second, the mortality assumption implicit in the guarantee did not anticipate the improvement in mortality which actually occurred.

The emerging liabilities under these guarantees threatened the solvency of some companies and led to the closure of Equitable Life (UK) to new business. In this paper we explore the pricing and risk management of these guarantees.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 33 , Issue 2 , November 2003 , pp. 125 - 152
Copyright
Copyright © ASTIN Bulletin 2003

Footnotes

1

Both authors acknowledge the support of the National Science and Engineering Research Council of Canada.

References

11. References

Ahn, D-H., Dittmar, R.F. and Gallant, A.R. (2002) Quadratic term structure models: theory and evidence. Review of Financial Studies 15, 243–288.CrossRefGoogle Scholar
Andersen, L. and Andreasen, J. (2001) “Factor dependence in bermudan swaptions: fact or fiction?” Journal of Financial Economics 62 3–37.CrossRefGoogle Scholar
Andersen, T.G., Benzoni, L. and Lund, J. (2002) An empirical investigation of continuous-time equity return models. J ournal of Finance, 1239–1284.CrossRefGoogle Scholar
Bakshi, G., Cao, C. and Chen, Z. (1997) Empirical performance of alternative option pricing models. Journal of Finance 52, 2003–2049.CrossRefGoogle Scholar
Bakshi, G., Cao, C. and Chen, Z. (2000) Pricing and hedging long-term options. Journal of Econometrics 94, 277–318.CrossRefGoogle Scholar
Ballotta, L. and Haberman, S. (2002) Valuation of guaranteed annuity options. Working Paper, Department of Actuarial Science and Statistics, City University, London, UK.Google Scholar
Bansal, R. and Zhou, H. (2002) Term structure of interest rates with regime shifts. Journal of Finance 57, 1997–2043.CrossRefGoogle Scholar
Björk, T. (1998) Arbitrage theory in continuous time. Oxford University Press.CrossRefGoogle Scholar
Bolton, M.J., Carr, D.H., Collis, P.A. et al (1997) Reserving for annuity guarantees. Report of the Annuity Guarantees Working Party, Institute of Actuaries, London, UK.Google Scholar
Boyle, P.P. and Emanuel, D. (1980) Discretely adjusted option hedges. Journal of Financial Economics 8, 259–282.CrossRefGoogle Scholar
Boyle, P.P. and Schwartz, E.S. (1977) Equilibrium prices of guarantees under equity-linked contracts, Journal ofRisk and Insurance 44, 4, 639–660.Google Scholar
Boyle, P.P., Cox, S., Dufresne, D., Gerber, H., Mueller, H., Pedersen, H., Pliska, S., Sherris, M., Shiu, E. and Tan, K.S. (1998) Financial Economics. The Actuarial Foundation, Chicago, USA.Google Scholar
Cannabero, E. (1995) Where do one-factor interest rate models fail? Journal of Fixed Income 5, 31–52.CrossRefGoogle Scholar
Chernof, M., Gallant, A.R., Ghysels, E. and Tauchen, G. (2001) Alternative models for stock price dynamics. Working Paper, University of North Carolina.CrossRefGoogle Scholar
Cox, J.C., Ingersoll, J.E. and Ross, S.A. (1985) A theory of the term structure of interest rates. Econometrica 53, 385–467.CrossRefGoogle Scholar
Dai, Q. and Singleton, K. (2000) Specification analysis of affine term structure models. Journal of Finance 55, 1943–1978.CrossRefGoogle Scholar
Dai, Q. and Singleton, K. (2003) Term structure dynamics in theory and reality. Review of Financial Studies, forthcoming.CrossRefGoogle Scholar
Driessen, J., Klaassen, P. and Melenberg, B. (2003) The performance of multi-factor term structure models for pricing and hedging caps and swaptions, Journal ofFinancial and Quantitative Analysis, forthcoming.CrossRefGoogle Scholar
Dunbar, N. (1999) Sterling Swaptions under New Scrutiny. Risk, December 33–35.Google Scholar
Fan, R., Gupta, A. and Ritchken, P. (2001) On the performance of multi-factor term structure models for pricing caps and swaptions, Working Paper Case Western University, Weatherhead School of Management.Google Scholar
Fisher, H.F. and Young, J. (1965) Actuarial Practice of Life Assurance, Cambridge University Press.Google Scholar
Gupta, A. and Subrahmanyam, M.G. (2001) An Examination of the Static and Dynamic Performance of Interest Rate Option Pricing Models in the Dollar Cap-Floor Markets. Working Paper, Case Western Reserve University, Weatherhead School of Management.Google Scholar
Hardy, M.R. (2003) Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance, Wiley.Google Scholar
Hull, J. (2002) Options Futures and Other Derivatives, Prentice Hall.Google Scholar
Hull, J. and White, A. (1990) “Pricing Interest Rate Derivative Securities”, Review of Financial Studies 3(4), 573–592.Google Scholar
Jamshidian, F. (1989) “An Exact Bond Option Formula”, Journal of Finance 44(1), 205–209.CrossRefGoogle Scholar
Jiang, G.J. and Oomen, R.C.A. (2002) Hedging Derivatives Risk, Working Paper, University of Arizona.Google Scholar
Litterman, T. and Scheinkman, J. (1991) Common factors affecting bond returns. Journal of Fixed Income 1, 62–74.CrossRefGoogle Scholar
Longstaff, F., Santa-Clara, P. and Schwartz, E. (2001) Throwing Away a Billion Dollars. Journal of Financial Economics 63, 39–66.CrossRefGoogle Scholar
Maturity Guarantees Working Party (MGWP) (1980) Report of the Maturity Guarantees Working Party. Journal of the Institute of Actuaries 107, 102–212.Google Scholar
Melino, A. and S., Turnbull, M. (1995) Mis-specification and the Pricing and Hedging of long-term Foreign Currency Options. Journal of International Money and Finance 14.3, 373–393.CrossRefGoogle Scholar
Milevsky, M.A., and Promislow, S.D. (2001) Mortality derivatives and the option to annuitize. Insurance: Mathematics and Economics 29(3), 299–316.Google Scholar
Nowman, K.B. (1997) Gaussian Estimation of Single-Factor Continuous Time Models of the Term Structure of Interest Rates. Journal of Finance 52, 1695–1706.CrossRefGoogle Scholar
Pelsser, A. (2003) Pricing and Hedging Guaranteed Annuity Options via Static Option Replication. Insurance: Mathematics and Economics, forthcoming.CrossRefGoogle Scholar
Vasicek, O.A. (1977) “An Equilibrium Characterization of the Term Structure”. Journal of Financial Economics 5, 177–188.CrossRefGoogle Scholar
Wilkie, A.D., Waters, H.R. and Yang, S. (2003) Reserving, Pricing and Hedging for Policies with Guaranteed Annuity Options. Paper presented to the Faculty of Actuaries, Edinburgh, January 2003. British Actuarial Journal, forthcoming.CrossRefGoogle Scholar
Yang, S. (2001) Reserving, Pricing and Hedging for Guaranteed Annuity Options. Phd Thesis, Department of Actuarial Mathematics and Statistics, Heriot Watt University, Edinburgh.Google Scholar
Yu, J. and Phillips, P. (2001) A Gaussian Approach for Continuous Time Models of the Short Term Interest Rates. The Econometrics Journal 4(2), 211–225.Google Scholar