Advertisement

European Actuarial Journal

, Volume 9, Issue 2, pp 445–461 | Cite as

On the optimal hedge ratio in index-based longevity risk hedging

  • Jackie LiEmail author
  • Chong It Tan
  • Sixian Tang
  • Jia Liu
Original Research Paper

Abstract

In an index-based longevity hedge, the so-called longevity basis risk arises from the potential mismatch between the hedging instrument and the annuity portfolio being hedged, due to the differences in the underlying populations and payoff structures. To reduce the impact of this longevity basis risk and increase the hedge effectiveness, an optimal position in the hedging instrument should be determined appropriately with regard to the nature of the two populations and also the timing of the payments. In this paper, we examine some analytical results on the optimal hedge ratio in hedging the longevity exposure of an annuity portfolio with index-based longevity- or mortality-linked securities. This optimal hedge ratio may serve as a convenient starting point for constructing an index-based hedge. We also conduct a cost–benefit analysis using different financial objectives. Our results are based on data of Australian public sector pensioners.

Keywords

Index-based longevity hedge Longevity swap S-forward q-forward Longevity basis risk 

Notes

Acknowledgements

The authors thank Mercer Australia for providing the mortality datasets to the Longevity Basis Risk research project (Phase 2), which contributes to some parts of this paper. The Phase 2 project was sponsored jointly by the Institute and Faculty of Actuaries (IFoA) and the Life and Longevity Markets Association (LLMA).

References

  1. 1.
    Blake D, Burrows W (2001) Survivor bonds: helping to hedge mortality risk. J Risk Insur 68(2):339–348CrossRefGoogle Scholar
  2. 2.
    Cairns AJG (2013) Robust hedging of longevity risk. J Risk Insur 80(3):621–648CrossRefGoogle Scholar
  3. 3.
    Cairns AJG, Blake D, Dowd K (2006) A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. J Risk Insur 73(4):687–718CrossRefGoogle Scholar
  4. 4.
    Cairns AJG, Blake D, Dowd K (2008) Modelling and management of mortality risk: a review. Scand Actuar J 2008(2–3):79–113MathSciNetCrossRefGoogle Scholar
  5. 5.
    Chan WS, Li JSH, Li J (2014) The CBD mortality indexes: modeling and applications. N Am Actuar J 18(1):38–58MathSciNetCrossRefGoogle Scholar
  6. 6.
    Coughlan GD, Epstein D, Sinha A, Honig P (2007) q-forwards: derivatives for transferring longevity and mortality risk, JPMorgan. http://www.lifemetrics.com. Accessed 1 Feb 2018
  7. 7.
    Coughlan GD, Khalaf-Allah M, Ye Y, Kumar S, Cairns AJG, Blake D, Dowd K (2011) Longevity hedging 101: a framework for longevity basis risk analysis and hedge effectiveness. N Am Actuar J 15(2):150–176MathSciNetCrossRefGoogle Scholar
  8. 8.
    Dowd K (2003) Survivor bonds: a comment on Blake and Burrows. J Risk Insur 70(2):339–348CrossRefGoogle Scholar
  9. 9.
    Haberman S, Kaishev V, Millossovich P, Villegas A, Baxter S, Gaches A, Gunnlaugsson S, Sison M (2014) Longevity basis risk: a methodology for assessing basis risk. CASS business school, Hymans Robertson LLP, Institute and Faculty of Actuaries, Life and Longevity Markets Association. https://www.actuaries.org.uk/learn-and-develop/research-and-knowledge/actuarial-research-centre-arc/commissioned-projects/longevity-basis-risk. Accessed 8 Nov 2015
  10. 10.
    Human Mortality Database (HMD) (2017) University of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Germany). http://www.mortality.org. Accessed 6 Apr 2017
  11. 11.
    James E, Song X (2001) Annuities markets around the world: money’s worth and risk intermediation. American Economic Association Meetings 2001. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.492.8023&rep=rep1&type=pdf. Accessed 13 Oct 2018
  12. 12.
    Keating C, Shadwick WF (2002) A universal performance measure. The Finance Development Centre, London. https://www.actuaries.org.uk/documents/universal-performance-measure. Accessed 13 Oct 2018
  13. 13.
    Kleinow T (2015) A common age effect model for the mortality of multiple populations. Insur Math Econ 63:147–152MathSciNetCrossRefGoogle Scholar
  14. 14.
    Koissi MC, Shapiro AF, Högnäs G (2006) Evaluating and extending the Lee-Carter model for mortality forecasting: bootstrap confidence interval. Insur Math Econ 38:1–20MathSciNetCrossRefGoogle Scholar
  15. 15.
    Lee RD, Carter LR (1992) Modeling and forecasting U.S. mortality. J Am Stat Assoc 87(419):659–671zbMATHGoogle Scholar
  16. 16.
    Li J (2014) A quantitative comparison of simulation strategies for mortality projection. Ann Actuar Sci 8(2):281–297CrossRefGoogle Scholar
  17. 17.
    Li J, Dacorogna M, Tan CI (2014) The impact of joint mortality modelling on hedging effectiveness of mortality derivatives. Longevity 10: Tenth International Longevity Risk and Capital Markets Solutions Conference, Cass Business School, City University of London. https://www.cass.city.ac.uk/faculties-and-research/centres/pensions-institute/events/longevity-10/programme. Accessed 4 Sept 2014
  18. 18.
    Li J, Li JSH, Tan CI, Tickle L (2018) Assessing basis risk in index-based longevity swap transactions. Ann Actuar Sci 2:22.  https://doi.org/10.1017/s1748499518000179 CrossRefGoogle Scholar
  19. 19.
    Li JSH, Luo A (2012) Key q-duration: a framework for hedging longevity risk. ASTIN Bull 42(2):413–452MathSciNetzbMATHGoogle Scholar
  20. 20.
    Life and Longevity Markets Association (LLMA) (2010) Technical note: the S-forward. https://llma.org/. Accessed 29 Oct 2010
  21. 21.
    Sortino FA, Price LN (1994) Performance measurement in a downside risk framework. J Invest 3(3):59–64CrossRefGoogle Scholar
  22. 22.
    Villegas AM, Haberman S, Kaishev VK, Millossovich P (2017) A comparative study of two-population models for the assessment of basis risk in longevity hedges. ASTIN Bull 47(3):631–679MathSciNetCrossRefGoogle Scholar
  23. 23.
    Zhou R, Li JSH, Tan KS (2013) Pricing standardized mortality securitizations: a two-population model with transitory jump effects. J Risk Insur 80(3):733–774CrossRefGoogle Scholar

Copyright information

© EAJ Association 2019

Authors and Affiliations

  1. 1.Department of Actuarial Studies and Business AnalyticsMacquarie UniversitySydneyAustralia

Personalised recommendations