×

Pension risk management with funding and buyout options. (English) Zbl 1398.91322

Summary: There has been a surge of interest in recent years from defined benefit pension plan sponsors in de-risking their plans with strategies such as “longevity hedges” and “pension buyouts” [Y. Lin et al., Insur. Math. Econ. 63, 52–65 (2015; Zbl 1348.91170)]. While buyouts are attractive in terms of value creation, they are capital intensive and expensive, particularly for firms with underfunded plans. The existing literature mainly focuses on the costs and benefits of pension buyouts. Little attention has been paid to how to capture the benefits of de-risking within a plan’s financial means, especially when buyout deficits are significant. To fill this gap, we propose two options, namely a pension funding option and pension buyout option, that provide financing for both underfunded and well funded plans to cover the buyout risk premium and the pension funding deficit, if a certain threshold is reached. To increase market liquidity, we create a transparent pension funding index, calculated from observed capital market indices and publicly available mortality tables as well as pension mandatory contributions, to determine option payoffs. A simulation based pricing framework is then introduced to determine the prices of the proposed pension options. Our numerical examples show that these options are effective and economically affordable. Moreover, our sensitivity analyses demonstrate the reliability of our pricing models.

MSC:

91B30 Risk theory, insurance (MSC2010)
91G20 Derivative securities (option pricing, hedging, etc.)

Citations:

Zbl 1348.91170
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Atanasova, C.V., Gatev, E., 2009. Risk taking and incentives of institutional investors: Evidence from US defined benefit plans, Working Paper, March.; Atanasova, C.V., Gatev, E., 2009. Risk taking and incentives of institutional investors: Evidence from US defined benefit plans, Working Paper, March.
[2] Bikker, J. A.; Broeders, D. W.; de Dreu, J., Stock market performance and pension fund investment policy: Rebalancing, free float, or market timing?, Int. J. Cent. Bank., 6, 2, 53-79 (2007)
[3] Bikker, J. A.; Broeders, D. W.G. A.; Hollanders, D. A.; Ponds, E. H.M., Pension funds’ asset allocation and participant age: A test of the life-cycle model, J. Risk Insurance, 79, 3, 595-618 (2012)
[4] Bo, L.; Wang, Y.; Yang, X., Markov-modulated jump-diffusions for currency option pricing, Insurance Math. Econom., 46, 3, 461-469 (2010) · Zbl 1231.91425
[5] Buckmann, C., 2014. De-risking your retiree pensions? Verizon court affirms plan sponsor rights to shed obligations, http://www.pensionsbenefitslaw.com; Buckmann, C., 2014. De-risking your retiree pensions? Verizon court affirms plan sponsor rights to shed obligations, http://www.pensionsbenefitslaw.com
[6] Bunkley, N., 2012. G.M. changes pensions for salaried workers. http://www.nytimes.com; Bunkley, N., 2012. G.M. changes pensions for salaried workers. http://www.nytimes.com
[7] Cox, J. C.; Ingersoll, J. E.; Ross, S. A., A theory of the term structure of interest rates, Econometrica, 53, 2, 385-407 (1985) · Zbl 1274.91447
[8] Cox, S. H.; Lin, Y., Natural hedging of life and annuity mortality risks, N. Am. Actuar. J., 11, 3, 1-15 (2007) · Zbl 1480.91196
[9] Cox, S. H.; Lin, Y.; Tian, R.; Yu, J., Managing capital market and longevity risks in a defined benefit pension plan, J. Risk Insurance, 80, 3, 585-619 (2013)
[10] Cox, S. H.; Lin, Y.; Tian, R.; Zuluaga, L. F., Portfolio risk management with CV a R-like constraints, N. Am. Actuar. J., 14, 1, 86-106 (2010) · Zbl 1219.91132
[11] Cox, S. H.; Lin, Y.; Tian, R.; Zuluaga, L. F., Mortality portfolio risk management, J. Risk Insurance, 80, 4, 853-890 (2013)
[12] Cox, S. H.; Lin, Y.; Wang, S., Multivariate exponential tilting and pricing implications for mortality securitization, J. Risk Insurance, 73, 4, 719-736 (2006)
[13] Dambra, M., 2014. The effect of internal capital shocks on manager behavior: evidence from changes in erisa pension accounting rules, March. Available at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2418341; Dambra, M., 2014. The effect of internal capital shocks on manager behavior: evidence from changes in erisa pension accounting rules, March. Available at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2418341
[14] Ebling, A., 2014. Companies prepare to dump pension plans in 2014. http://onforb.es/1fHDdNH; Ebling, A., 2014. Companies prepare to dump pension plans in 2014. http://onforb.es/1fHDdNH
[15] Gerber, H. U.; Shiu, E. S., Option pricing by esscher transforms, Trans. Soc. Actuar., 46, 99-191 (1994)
[16] Gükaynak, R. S.; Sack, B.; Swanson, E., The sensitivity of long-term interest rates to economic news: Evidence and implications for macroeconomic models, Amer. Econ. Rev., 95, 1, 425-436 (2005)
[17] Hull, J.; White, A., Pricing interest-rate-derivative securities, Rev. Financ. Stud., 3, 4, 573-592 (1990) · Zbl 1386.91152
[18] Lam, J., The CRO is here to stay, Risk Manag., 48, 4, 16-20 (2001)
[19] LCP, 2012. LCP pension buy-ins, buy-outs and longevity swaps 2012. http://www.lcp.uk.com; LCP, 2012. LCP pension buy-ins, buy-outs and longevity swaps 2012. http://www.lcp.uk.com
[20] Lee, R. D.; Carter, L., Modelling and forecasting the time series of US mortality, J. Amer. Statist. Assoc., 87, 419, 659-671 (1992) · Zbl 1351.62186
[21] Liebenberg, A. P.; Hoyt, R. E., The determinants of enterprise risk management: Evidence from the appointment of chief risk officers, Risk Manage. Insur. Rev., 6, 1, 37-52 (2003)
[22] Lin, Y.; Cox, S. H., Securitization of mortality risks in life annuities, J. Risk Insurance, 72, 2, 227-252 (2005)
[23] Lin, Y.; Cox, S. H., Securitization of catastrophe mortality risks, Insurance Math. Econom., 42, 2, 628-637 (2008) · Zbl 1152.91593
[24] Lin, Y.; Liu, S.; Yu, J., Pricing mortality securities with correlated mortality indices, J. Risk Insurance, 80, 4, 921-948 (2013)
[25] Lin, Y.; MacMinn, R. D.; Tian, R., De-risking defined benefit plans, Insurance Math. Econom., 63, 52-65 (2015) · Zbl 1348.91170
[26] Lin, Y.; MacMinn, R. D.; Tian, R.; Yu, J., Pension risk management in the enterprise risk management framework, J. Risk Insurance, 84, 345-365 (2017)
[27] Lin, Y.; Shi, T.; Arik, A., Pricing buy-ins and buy-outs, J. Risk Insurance, 84, 367-392 (2017)
[28] Lin, Y.; Tan, K. S.; Tian, R.; Yu, J., Downside risk management of a defined benefit plan considering longevity basis risk, N. Am. Actuar. J., 18, 1, 68-86 (2014) · Zbl 1412.91048
[29] Longstaff, F. A.; Schwartz, E. S., Interest rate volatility and the term structure: a two-factor general equilibrium model, J. Finance, 47, 4, 1259-1282 (1992)
[30] Lucas, D., Zeldes, S.P., 2006. Valuing and hedging defined benefit pension obligations—the role of stocks, Working Paper, Northwestern University.; Lucas, D., Zeldes, S.P., 2006. Valuing and hedging defined benefit pension obligations—the role of stocks, Working Paper, Northwestern University.
[31] Mathur, R., Kaplan, S., 2013. Reducing pension risk: The myths holding back plan sponsors. http://pensionrisk.prudential.com; Mathur, R., Kaplan, S., 2013. Reducing pension risk: The myths holding back plan sponsors. http://pensionrisk.prudential.com
[32] Maurer, R.; Mitchell, O. S.; Rogalla, R., Managing contribution and capital market risk in a funded public defined benefit plan: Impact of CV aR cost constraints, Insurance Math. Econom., 45, 1, 25-34 (2009) · Zbl 1231.91216
[33] McDonald, R. L., Derivatives Markets (2013), Pearson
[34] Mercer LLC, 2014. Mercer global pension buyout index, December. http://www.mercer.com/newsroom/mercer-global-pension-buyout-index.html; Mercer LLC, 2014. Mercer global pension buyout index, December. http://www.mercer.com/newsroom/mercer-global-pension-buyout-index.html
[35] Merton, R. C., Option pricing when underlying stock returns are discontinuous, J. Financ. Econ., 3, 1-2, 125-144 (1976) · Zbl 1131.91344
[36] Milidonis, A.; Lin, Y.; Cox, S. H., Mortality regimes and pricing, N. Am. Actuar. J., 15, 2, 266-289 (2011) · Zbl 1228.91043
[37] Milliman,, 2015. Milliman analysis: January 2015 interest rates reach a record low of 3.38
[38] Nocco, B. W.; Stulz, R. M., Enterprise risk management: Theory and practice, J. Appl. Corp. Finance, 18, 4, 8-20 (2006)
[39] Petersen, M. A., Pension reversions and worker-stockholder wealth transfers, Quart. J. Econ., 107, 1033-1056 (1992)
[40] Rauh, J. D., Risk shifting versus risk management: investment policy in corporate pension plans, Rev. Financ. Stud., 22, 7, 2687-2733 (2009)
[41] Wang, S. S., Premium calculation by transforming the layer premium density, ASTIN Bull., 26, 1, 71-92 (1996)
[42] Wang, S. S., A class of distortion operations for pricing financial and insurance risks, J. Risk Insurance, 67, 1, 15-36 (2000)
[43] Wang, S. S., A universal framework for pricing financial and insurance risks, ASTIN Bull., 32, 2, 213-234 (2002) · Zbl 1090.91555
[44] Ward, M., 2014. 2014 annual buyout market watch report. http://www.jltgroup.com/content/UK; Ward, M., 2014. 2014 annual buyout market watch report. http://www.jltgroup.com/content/UK
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.