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Valuation of risk-based premium of DB pension plan with terminations

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Listed:
  • Qian, Linyi
  • Shen, Yang
  • Wang, Wei
  • Yang, Zhixin

Abstract

This paper concentrates on the premium valuation of pension insurance provided by the Pension Benefit Guaranty Corporation (PBGC). The PBGC provides a defined benefit pension sponsor with coverage in case that the pension fund fails to make pension payments as promised or that the plan sponsor does not stay in business any more. In practice, both the pension fund and the sponsor assets play a critical role in fulfilling the commitment of pension payments, and thereby it is not reasonable to isolate the risk of distress termination of the sponsor assets from that of the premature termination of the pension fund. Different from previous works in which the premature termination of the pension fund and the distress termination of the sponsor assets are analyzed separately, our model examines the situation in which retirees suffer the risk of two types of terminations at the same time. We evaluate the risk-based fair premium under the framework that the pension fund and the sponsor assets are correlated and subject to the risk of the involuntary termination (i.e., premature termination) and the distress termination, respectively. In this framework, we manage to obtain closed-form pricing formulas. Our model is more practical because of the realistic design of termination schemes. Numerical simulations are also carried out to demonstrate our findings. Our numerical experiments validate that a variable rate premium is more appropriate for the PBGC to implement.

Suggested Citation

  • Qian, Linyi & Shen, Yang & Wang, Wei & Yang, Zhixin, 2019. "Valuation of risk-based premium of DB pension plan with terminations," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 51-63.
    • Handle: RePEc:eee:insuma:v:86:y:2019:i:c:p:51-63
    DOI: 10.1016/j.insmatheco.2019.01.012
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    References listed on IDEAS

    as
    1. Chunli Cheng & Filip Uzelac, 2018. "A Termination Rule for Pension Guarantee Funds," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(1), pages 275-300, March.
    2. Metzler, Adam, 2010. "On the first passage problem for correlated Brownian motion," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 277-284, March.
    3. David A. Love & Paul A. Smith & David W. Wilcox, 2009. "Should risky firms offer risk-free DB pensions?," Finance and Economics Discussion Series 2009-20, Board of Governors of the Federal Reserve System (U.S.).
    4. Kalra, Raman & Jain, Gautam, 1997. "A continuous-time model to determine the intervention policy for PBGC," Journal of Banking & Finance, Elsevier, vol. 21(8), pages 1159-1177, August.
    5. Chen, An & Uzelac, Filip, 2014. "A risk-based premium: What does it mean for DB plan sponsors?," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 1-11.
    6. Alan Marcus, 1987. "Corporate Pension Policy and the Value of PBGC Insurance," NBER Chapters, in: Issues in Pension Economics, pages 49-80, National Bureau of Economic Research, Inc.
    7. Jeffrey R. Brown, 2008. "Guaranteed Trouble: The Economic Effects of the Pension Benefit Guaranty Corporation," Journal of Economic Perspectives, American Economic Association, vol. 22(1), pages 177-198, Winter.
    8. Christopher M. Lewis & George Pennacchi, 1994. "The value of Pension Benefit Guaranty Corporation insurance," Proceedings, Federal Reserve Bank of Cleveland, pages 735-756.
    9. Zvi Bodie, 2006. "On asset-liability matching and federal deposit and pension insurance," Review, Federal Reserve Bank of St. Louis, vol. 88(Jul), pages 323-330.
    10. Chen, An, 2011. "A risk-based model for the valuation of pension insurance," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 401-409.
    11. Sharpe, William F., 1976. "Corporate pension funding policy," Journal of Financial Economics, Elsevier, vol. 3(3), pages 183-193, June.
    12. Bodie, Zvi & Shoven, John B. & Wise, David A. (ed.), 1987. "Issues in Pension Economics," National Bureau of Economic Research Books, University of Chicago Press, edition 1, number 9780226062846.
    13. David W. Wilcox, 2006. "Reforming the Defined-Benefit Pension System," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 37(1), pages 235-304.
    14. Dirk Broeders & An Chen, 2013. "Pension Benefit Security: A Comparison of Solvency Requirements, a Pension Guarantee Fund, and Sponsor Support," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(2), pages 239-272, June.
    15. Fiona Stewart, 2007. "Benefit Security Pension Fund Guarantee Schemes," OECD Working Papers on Insurance and Private Pensions 5, OECD Publishing.
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    More about this item

    Keywords

    Defined benefit pension plan; PBGC; Risk-based premium; Distress termination; Premature termination;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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