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DYNAMIC HEDGING STRATEGIES FOR CASH BALANCE PENSION PLANS

Published online by Cambridge University Press:  11 June 2018

Xiaobai Zhu ,
Mary R. Hardy  and
David Saunders
Xiaobai Zhu
Affiliation:
Dept of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada Email: [email protected]
Mary R. Hardy*
Affiliation:
Dept of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada
David Saunders
Affiliation:
Dept of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada Email: [email protected]
*
Email: [email protected]
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Abstract

Cash balance pension plans with crediting rates linked to long bond yields are relatively common in the United States, but their liabilities are proving very challenging to hedge. In this paper, we consider dynamic hedge strategies using the one-factor and two-factor Hull White models, based on results for the liability valuation from Hardy et al. (2014). The strategies utilise simple hedge portfolios combining one or two zero-coupon bonds, and a money market account. We assess the effectiveness of the strategies by considering how accurately each one would have hedged a 5-year cash balance liability through the past 20 years, using real-world returns and crediting rates, and assuming parameters calibrated using the information available at the time. We show that there is considerable impact of model and parameter uncertainty, with additional, less severe impact from discrete hedging error and transactions costs. Despite this, the dynamic hedge strategies do manage to stabilize surplus substantially, even through the turbulence of the past two decades.

Keywords

Cash balance pensiondynamic hedgingHull-White model
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 3 , September 2018 , pp. 1245 - 1275
Copyright
Copyright © Astin Bulletin 2018 

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References

Biggs, A. (2010) An options pricing method for calculating the market price of public sector pension liabilities. American Enterprise Institute Working Paper 164.Google Scholar
Biggs, A. and Smetters, K. (2013) Understanding the Argument for Market Valuation of Public Pension Liabilities. Washington, DC: American Enterprise Institute.Google Scholar
Björk, T. (2009) Arbitrage Theory in Continuous Time. Oxford, UK: Oxford University Press.Google Scholar
Boyle, P. and Hardy, M.R. (2003) Guaranteed annuity options. ASTIN Bulletin, 33 (2), 125–152.Google Scholar
Brigo, D. and Mercurio, F. (2001) Interest Rate Models: Theory and Practice – With Smile, Inflation and Credit. New York, NY, USA: Springer-Verlag.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), 50–62.Google Scholar
Chen, K. and Hardy, M.R. (2009) The DB underpin hybrid pension plan: Fair valuation and funding. North American Actuarial Journal, 13 (4), 407–424.Google Scholar
Coronado, J.L. and Copeland, P.C. (2003) Cash balance pension plan conversions and the new economy. Technical report, Federal Reserve Board Finance and Economics Discussion Series. Working Paper No. 2003–63.Google Scholar
Dickson, D.C., Hardy, M.R. and Waters, H.R. (2013) Actuarial Models for Life Contingent Risk (2nd Edition). Cambridge, UK: Cambridge University Press.Google Scholar
Driessen, J., Klaassen, P. and Meleberg, B. (2003) The performance of multi-factor term structure models for pricing and hedging caps and swaptions. Journal of Financial and Quantitative Analysis, 38 (3), 635–672.Google Scholar
Enev, E. (2011) Gaussian Affine Term Structure Models Within the Duffie-Kan Framework and Their Use for Forecasting. Master's thesis, University of Amsterdam.Google Scholar
Fan, R., Gupta, A. and Ritchken, P. (2007) On pricing and hedging in the swaption market: How many factors really? The Journal of Derivatives, 15 (1), 9–33.Google Scholar
Glasserman, P. (2003) Monte Carlo Methods in Financial Engineering. New York: Springer-Verlag.Google Scholar
Gold, J. (2001) Shareholder-optimal design of cash balance pension plans. Pension Research Council. Working Paper 2001–7.Google Scholar
Gupta, A. and Subrahmanyam, M. (2005) Pricing and hedging interest rate options: Evidence from cap-floor markets. Journal of Banking and Finance, 29, 701–733.Google Scholar
Gurrieri, S., Nakabayashi, M. and Wong, T. (2009) Calibration methods of hull-white model. SSRN Electronic Journal. ISSN 1556–5068.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), 294–314.Google Scholar
Harvey, J. (2012) Strategies for hedging interest rate risk in a cash balance plan. Technical report, Russell Investments Research.Google Scholar
Kravitz (2012) 2012 National CASH BALANCE research report. Technical report, Kravitz, Inc.Google Scholar
Kravitz (2015) 2015 National CASH BALANCE research report. Technical report, Kravitz, Inc.Google Scholar
Liu, Y. (2010) Pricing and Hedging the Guaranteed Minimum Withdrawal Benefits in Variable Annuities. Ph.D. thesis, University of Waterloo.Google Scholar
Marshall, C. (2011) Financial Risk Management of Guaranteed Minimum Income Benefits Embedded in Variable Annuities. Ph.D. thesis, University of Waterloo.Google Scholar
Murphy, R.J. (2001) The cash balance funding method. In Cash Balance Symposium Monograph. Schaumburg, IL: Society of Actuaries.Google Scholar
Niehaus, G. and Yu, T. (2005) Cash-Balance plan conversions: Evidence on excise taxes and implicit contracts. Journal of Risk & Insurance, 72 (2), 321–352.Google Scholar
Novy-Marx, R. and Rauh, Joshua D. (2009) The liability and risks of state-sponsored pension plans. Journal of Economic Perspectives, 23 (4), 191–210.Google Scholar
PricewaterhouseCoopers (2014) Embedded options in pension plans – valuation of guarantees in cash balance plans. Technical report, Society of Actuaries, Schaumburg, IL.Google Scholar
Rogerscasey, S. (2015) Examining cash-balance plans' investment risk. Technical report, Segal Rogerscasey Investment Brief.Google Scholar
Schrager, David F. and Pelsser, Antoon A. (2006) Pricing swaptions and coupon bond options in affine term structure models. Mathematical Finance, 16 (4), 673–694.Google Scholar
Zhu, X. (2015) Performance of Dynamic Hedging Strategies for Cash Balance Pension Plans. Master's thesis, University of Waterloo.Google Scholar