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Subjective value of the guarantees embedded in public cash-balance pension plans

Published online by Cambridge University Press:  23 February 2017

CHUN-HUA TANG*
Affiliation:
Department of Finance, National Sun Yat-sen University, Kaohsiung, Taiwan (e-mail: chtang@mail.nsysu.edu.tw)

Abstract

Some public sectors provide cash-balance pension plans with guaranteed interest credits. We use the certainty-equivalence framework to derive the subjective value of the guarantee perceived by the participant. Numerical results show that in many scenarios the subjective value is lower than the cost of the guarantee derived by option pricing approaches, implying that public sectors potentially spend too much in providing the guarantee. However, the subjective value could be higher than the cost of the guarantee under some scenarios, depending on the participant's level of risk aversion, the feasibility of diversification, and so forth.

Type
Article
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

I gratefully acknowledge the financial support from the Ministry of Science and Technology (formerly known as National Science Council) of Taiwan (NSC 98-2410-H-035-010).

References

Baker, M., Bradley, B. and Wurgler, J. (2011) Benchmarks as limits to arbitrage: understanding the low-volatility anomaly. Financial Analysts Journal, 67(1): 4054.Google Scholar
Black, F. and Scholes, M. (1973) The pricing of options and corporate liabilities. Journal of Political Economy, 81: 637654.Google Scholar
Branger, N., Mahayni, A. and Schneider, J. (2010) On the optimal design of insurance contracts with guarantees. Insurance: Mathematics and Economics, 46: 485492.Google Scholar
Brown, D. T., Dybvig, P. H. and Marshall, W. J. (2001) The cost and duration of cash-balance pension plans. Financial Analysts Journal, 57(6): 5062.Google Scholar
Cai, J. and Vijh, A. (2005) Executive stock and option valuation in a two state-variable framework. Journal of Derivatives, 12(3): 927.Google Scholar
Clark, R. L. and Schieber, S. J. (2004) Adopting cash balance pension plans: implications and issues. Journal of Pension Economics and Finance, 3: 271295.Google Scholar
Coronado, J. L. and Copeland, P. C. (2004) Cash balance pension plan conversions and the new economy. Journal of Pension Economics and Finance, 3: 297314.Google Scholar
Deelstra, G. and Rayée, G. (2013) Pricing variable annuity guarantees in a local volatility framework. Insurance: Mathematics and Economics, 53: 650663.Google Scholar
Gao, J. and Ulm, E. R. (2012) Optimal consumption and allocation in variable annuities with Guaranteed Minimum Death Benefits. Insurance: Mathematics and Economics, 51: 586598.Google Scholar
Graham, J. R. and Harvey, C. R. (2013) The equity risk premium in 2013. Working paper, available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2206538 Google Scholar
Grosen, A. and Jørgensen, P. L. (1997) Valuation of early exercisable interest rate guarantees. Journal of Risk and Insurance, 64: 481503.Google Scholar
Grosen, A. and 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: 3757.Google Scholar
Hall, B. J. and Murphy, K. J. (2000) Optimal exercise prices for executive stock options. American Economic Review, 90: 209214.Google Scholar
Hardy, M. R., Saunders, D. and Zhu, X. (2014) Market-consistent valuation and funding of cash balance pensions. North American Actuarial Journal, 18(2): 294314.Google Scholar
Harper, J. T. and Treanor, S. D. (2014) Pension conversion, termination, and wealth transfers. Journal of Risk and Insurance, 81: 177198.Google Scholar
Hilliard, J. E. and Hilliard, J. (2015) Estimating early exercise premiums on gold and copper options using a multifactor model and density matched lattices. Financial Review, 50: 2756.Google Scholar
Hürlimann, W. (2010) Analytical pricing of the unit-linked endowment with guarantees and periodic premiums. Astin Bulletin, 40(2): 631653.Google Scholar
Inkmann, J., Lopes, P. and Michaelides, A. (2011) How deep is the annuity market participation puzzle? Review of Financial Studies, 24: 279319.Google Scholar
Lambert, R. A., Larcker, D. F. and Verrecchia, R. E. (1991) Portfolio considerations in valuing executive compensation. Journal of Accounting Research, 29: 129149.Google Scholar
Lindset, S. (2003) Pricing of multi-period rate of return guarantees. Insurance: Mathematics and Economics, 33: 629644.Google Scholar
Lindset, S. (2004) Relative guarantees. Geneva Papers on Risk and Insurance Theory, 29: 187209.Google Scholar
Niehaus, G. and Yu, T. (2005) Cash-balance plan conversions: evidence on excise taxes and implicit contracts. Journal of Risk and Insurance, 72: 321352.Google Scholar
Nielsen, J. A., Sandmann, K. and Schlögl, E. (2011) Equity-linked pension schemes with guarantees. Insurance: Mathematics and Economics, 49: 547564.Google Scholar
U.S. Bureau of Labor Statistics (2013) Economic news release: consumer expenditures midyear update -- July 2011 through June 2012 average, available at http://www.bls.gov/news.release/archives/cesmy_03272013.htm Google Scholar
Vasicek, O. (1977) An equilibrium characterization of the term structure. Journal of Financial Economics, 5: 177188.Google Scholar
Wang, T. and Young, V. R. (2011) Maximizing the utility of consumption with commutable life annuities. Insurance: Mathematics and Economics, 51: 352369.Google Scholar
Yang, S., Yueh, M. and Tang, C. (2008) Valuation of the interest rate guarantee embedded in defined contribution pension plans. Insurance: Mathematics and Economics, 42: 920934.Google Scholar