Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-54vk6 Total loading time: 0.272 Render date: 2022-08-10T07:41:16.497Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

STATE-DEPENDENT FEES FOR VARIABLE ANNUITY GUARANTEES

Published online by Cambridge University Press:  19 May 2014

Carole Bernard
Affiliation:
Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterloo, Ontario, Canada E-Mail: c3bernar@uwaterloo.ca
Mary Hardy
Affiliation:
Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterloo, Ontario, Canada E-Mail: mrhardy@uwaterloo.ca
Anne Mackay*
Affiliation:
Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterloo, Ontario, Canada

Abstract

For variable annuity policies, management fees for the most basic guarantees are charged at a constant rate throughout the term of the policy. This creates a misalignment of risk and income – the fee income is low when the option value is high, and vice versa. In turn, this may create adverse incentives for policyholders, for example, encouraging surrenders when the options are far out-of-the-money.

In this paper, we explore a new fee structure for variable annuities, where the fee rate supporting the cost of guarantees depends on the moneyness of those guarantees. We derive formulas for calculating the fee rates assuming fees are paid only when the guarantees are in-the-money, or are close to being in-the-money, and we illustrate with some numerical examples. We investigate the effect of this new fee structure on the surrender decision.

Type
Research Article
Copyright
Copyright © ASTIN Bulletin 2014 

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., Millossovich, P., Olivieri, A. and Pitacco, E. (2011) Variable annuities: A unifying valuation approach. Insurance: Mathematics and Economics, 49 (3), 285297.Google Scholar
Bauer, D., Kling, A. and Russ, J. (2008) A universal pricing framework for guaranteed minimum benefits in variable annuities. Astin Bulletin, (38), 621651CrossRefGoogle Scholar
Belanger, A., Forsyth, P. and Labahn, G. (2009) Valuing the guaranteed minimum death benefit clause with partial withdrawals. Applied Mathematical Finance, 16 (6), 451496.CrossRefGoogle Scholar
Bernard, C. and MacKay, A. (2014) Reducing surrender incentives through fee structure in variable annuities. In Proceedings of the Risk Management Reloaded Conference.Google Scholar
Bernard, C., MacKay, A. and Muehlbeyer, M. (2014) Optimal surrender policy for variable annuity guarantees. Insurance: Mathematics and Economics 55, 116128.Google Scholar
Boyle, P.P. and Hardy, M.R. (2003) Guaranteed annuity options. Astin Bulletin, 33 (2), 125152.CrossRefGoogle Scholar
Chen, Z., Vetzal, K. and Forsyth, P.A. (2008) “The effect of modelling parameters on the value of GMWB guarantees. Insurance: Mathematics and Economics, 43 (1), 165173.Google Scholar
Coleman, T., Kim, Y., Li, Y. and M Patron, M. (2007) Robustly hedging variable annuities with guarantees under jump and volatility risks. Journal of Risk and Insurance, 74 (2), 347376.CrossRefGoogle Scholar
Dai, M., Kuen Kwok, Y. and Zong, J. (2008) Guaranteed minimum withdrawal benefit in variable annuities. Mathematical Finance, 18 (4), 595611.CrossRefGoogle Scholar
Dickson, D.C.M., Hardy, M.R. and Waters, H. (2009) Actuarial Mathematics for Life Contingent Risks. Cambridge, England: Cambridge University Press.CrossRefGoogle Scholar
Hardy, M.R. (2001) A regime-switching model of long-term stock returns. North American Actuarial Journal, 5 (2), 4153.CrossRefGoogle Scholar
Hardy, M.R. (2003) Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance. Hoboken, New Jersey: John Wiley & Sons, Inc.Google Scholar
Karatzas, I. and Shreve, S.E. (1984) Trivariate density of Brownian motion, its local and occupation times, with application to stochastic control. Annals of Probability, 12 (3), 819828.CrossRefGoogle Scholar
Karatzas, I. and Shreve, S.E. (1991) Brownian Motion and Stochastic Calculus, 2nd ed.New York: Springer.Google Scholar
Kim, I.J. and Yu, G.G. (1996) An alternative approach to the valuation of American options and applications. Review of Derivatives Research, 1 (1), 6185.CrossRefGoogle Scholar
Marshall, C., Hardy, M.R. and Saunders, D. (2010) Valuation of a guaranteed minimum income benefit. North American Actuarial Journal, 14 (1), 3858.CrossRefGoogle Scholar
Milevsky, M.A. and Salisbury, T.S. (2001) The real option to Lapse a variable annuity: Can surrender charges complete the market. In Conference Proceedings of the 11th Annual International AFIR Colloquium.Google Scholar
Moenig, T. and Bauer, D. (2012) Revisiting the risk-neutral approach to optimal policyholder behavior: A study of withdrawal guarantees in variable annuities, Working Paper, Georgia State University.Google Scholar
Palmer, B. (2006) “Equity-indexed annuities: Fundamental concepts and issues, Working Paper.Google Scholar
Prudential(UK) (2012) Key Features of the Flexible Investment Plan (No Initial Charge and Initial Charge option) - Additional Investments, www.pru.co.uk/pdf/FIPK10080.pdf; Retrieved February 27, 2013.Google Scholar
27
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org 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 saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ 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.

STATE-DEPENDENT FEES FOR VARIABLE ANNUITY GUARANTEES
Available formats
×

Save article to Dropbox

To save 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 used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

STATE-DEPENDENT FEES FOR VARIABLE ANNUITY GUARANTEES
Available formats
×

Save article to Google Drive

To save 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 used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

STATE-DEPENDENT FEES FOR VARIABLE ANNUITY GUARANTEES
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *