Skip to main content

Guaranteed Annuity Options

  • Phelim Boyle (a1) and Mary Hardy (a2)

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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Guaranteed Annuity Options
      Available formats
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Guaranteed Annuity Options
      Available formats
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Guaranteed Annuity Options
      Available formats
Hide All
Ahn D-H., Dittmar R.F. and Gallant A.R. (2002) Quadratic term structure models: theory and evidence. Review of Financial Studies 15, 243288.
Andersen L. and Andreasen J. (2001) “Factor dependence in bermudan swaptions: fact or fiction?Journal of Financial Economics 62 337.
Andersen T.G., Benzoni L. and Lund J. (2002) An empirical investigation of continuous-time equity return models. J ournal of Finance, 12391284.
Bakshi G., Cao C. and Chen Z. (1997) Empirical performance of alternative option pricing models. Journal of Finance 52, 20032049.
Bakshi G., Cao C. and Chen Z. (2000) Pricing and hedging long-term options. Journal of Econometrics 94, 277318.
Ballotta L. and Haberman S. (2002) Valuation of guaranteed annuity options. Working Paper, Department of Actuarial Science and Statistics, City University, London, UK.
Bansal R. and Zhou H. (2002) Term structure of interest rates with regime shifts. Journal of Finance 57, 19972043.
Björk T. (1998) Arbitrage theory in continuous time. Oxford University Press.
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.
Boyle P.P. and Emanuel D. (1980) Discretely adjusted option hedges. Journal of Financial Economics 8, 259282.
Boyle P.P. and Schwartz E.S. (1977) Equilibrium prices of guarantees under equity-linked contracts, Journal ofRisk and Insurance 44, 4, 639660.
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.
Cannabero E. (1995) Where do one-factor interest rate models fail? Journal of Fixed Income 5, 3152.
Chernof M., Gallant A.R., Ghysels E. and Tauchen G. (2001) Alternative models for stock price dynamics. Working Paper, University of North Carolina.
Cox J.C., Ingersoll J.E. and Ross S.A. (1985) A theory of the term structure of interest rates. Econometrica 53, 385467.
Dai Q. and Singleton K. (2000) Specification analysis of affine term structure models. Journal of Finance 55, 19431978.
Dai Q. and Singleton K. (2003) Term structure dynamics in theory and reality. Review of Financial Studies, forthcoming.
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.
Dunbar N. (1999) Sterling Swaptions under New Scrutiny. Risk, December 3335.
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.
Fisher H.F. and Young J. (1965) Actuarial Practice of Life Assurance, Cambridge University Press.
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.
Hardy M.R. (2003) Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance, Wiley.
Hull J. (2002) Options Futures and Other Derivatives, Prentice Hall.
Hull J. and White A. (1990) “Pricing Interest Rate Derivative Securities”, Review of Financial Studies 3(4), 573592.
Jamshidian F. (1989) “An Exact Bond Option Formula”, Journal of Finance 44(1), 205209.
Jiang G.J. and Oomen R.C.A. (2002) Hedging Derivatives Risk, Working Paper, University of Arizona.
Litterman T. and Scheinkman J. (1991) Common factors affecting bond returns. Journal of Fixed Income 1, 6274.
Longstaff F., Santa-Clara P. and Schwartz E. (2001) Throwing Away a Billion Dollars. Journal of Financial Economics 63, 3966.
Maturity Guarantees Working Party (MGWP) (1980) Report of the Maturity Guarantees Working Party. Journal of the Institute of Actuaries 107, 102212.
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, 373393.
Milevsky M.A., and Promislow S.D. (2001) Mortality derivatives and the option to annuitize. Insurance: Mathematics and Economics 29(3), 299316.
Nowman K.B. (1997) Gaussian Estimation of Single-Factor Continuous Time Models of the Term Structure of Interest Rates. Journal of Finance 52, 16951706.
Pelsser A. (2003) Pricing and Hedging Guaranteed Annuity Options via Static Option Replication. Insurance: Mathematics and Economics, forthcoming.
Vasicek O.A. (1977) “An Equilibrium Characterization of the Term Structure”. Journal of Financial Economics 5, 177188.
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.
Yang S. (2001) Reserving, Pricing and Hedging for Guaranteed Annuity Options. Phd Thesis, Department of Actuarial Mathematics and Statistics, Heriot Watt University, Edinburgh.
Yu J. and Phillips P. (2001) A Gaussian Approach for Continuous Time Models of the Short Term Interest Rates. The Econometrics Journal 4(2), 211225.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
  • URL: /core/journals/astin-bulletin-journal-of-the-iaa
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 83 *
Loading metrics...

Abstract views

Total abstract views: 136 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd November 2017. This data will be updated every 24 hours.