Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-23T21:57:46.607Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymmetry in mortality volatility and its implications on index-based longevity hedging

Published online by Cambridge University Press:  05 May 2020

Kenneth Q. Zhou  and
Johnny Siu-Hang Li
Kenneth Q. Zhou
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Ontario, Canada School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA
Johnny Siu-Hang Li*
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Ontario, Canada Department of Economics, University of Melbourne, Melbourne, Australia
*
* Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Mortality volatility is crucially important to many aspects of index-based longevity hedging, including instrument pricing, hedge calibration and hedge performance evaluation. This paper sets out to develop a deeper understanding of mortality volatility and its implications on index-based longevity hedging. First, we study the potential asymmetry in mortality volatility by considering a wide range of generalised autoregressive conditional heteroskedasticity (GARCH)-type models that permit the volatility of mortality improvement to respond differently to positive and negative mortality shocks. We then investigate how the asymmetry of mortality volatility may impact index-based longevity hedging solutions by developing an extended longevity Greeks framework, which encompasses longevity Greeks for a wider range of GARCH-type models, an improved version of longevity vega, and a new longevity Greek known as “dynamic Delta”. Our theoretical work is complemented by two real-data illustrations, the results of which suggest that the effectiveness of an index-based longevity hedge could be significantly impaired if the asymmetry in mortality volatility is not taken into account when the hedge is calibrated.

Keywords

GARCH-type modelsLongevity GreeksS-forwardsValue-at-RiskThe Lee–Carter model
Type
Paper
Information
Annals of Actuarial Science , Volume 14 , Issue 2 , September 2020 , pp. 278 - 301
Copyright
© Institute and Faculty of Actuaries 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Badescu, A., Elliott, R.J. & Ortega, J.-P. (2014). Quadratic hedging schemes for non-Gaussian GARCH models. Journal of Economic Dynamics and Control, 42, 13–32.CrossRefGoogle Scholar
Bekaert, G. & Wu, G. (2000). Asymmetric volatility and risk in equity markets. Review of Financial Studies, 13(1), 1–42.CrossRefGoogle Scholar
Biffis, E. & Blake, D. (2014). Keeping some skin in the game: how to start a capital market in longevity risk transfers. North American Actuarial Journal, 18(1), 14–21.10.1080/10920277.2013.872552CrossRefGoogle Scholar
Blake, D., Cairns, A., Coughlan, G., Dowd, K. & Macminn, R. (2013). The new life market. Journal of Risk and Insurance, 80(3), 501–557.10.1111/j.1539-6975.2012.01514.xCrossRefGoogle Scholar
Brouhns, N., Denuit, M. & Vermunt, J.K. (2002). A poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31(3), 373–393.Google Scholar
Cairns, A.J. (2011). Modelling and management of longevity risk: approximations to survivor functions and dynamic hedging. Insurance: Mathematics and Economics, 49(3), 438–453.Google Scholar
Cairns, A.J. (2013). Robust hedging of longevity risk. Journal of Risk and Insurance, 80(3), 621–648.CrossRefGoogle Scholar
Cairns, A.J., Blake, D. & Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73(4), 687–718.CrossRefGoogle Scholar
Cairns, A.J., Dowd, K., Blake, D. & Coughlan, G.D. (2014). Longevity hedge effectiveness: a decomposition. Quantitative Finance, 14(2), 217–235.CrossRefGoogle Scholar
Campbell, J.Y. & Hentschel, L. (1992). No news is good news: an asymmetric model of changing volatility in stock returns. Journal of Financial Economics, 31(3), 281–318.CrossRefGoogle Scholar
Chai, C.M.H., Siu, T.K., Zhou, X., Hui, M., Chai, C.M.H., Kuen, T. & Xian, S. (2013). A double-exponential GARCH model for stochastic mortality. European Actuarial Journal, 3(2), 385–406.CrossRefGoogle Scholar
Chen, H., MacMinn, R. & Sun, T. (2015). Multi-population mortality models: a factor copula approach. Insurance: Mathematics and Economics, 63, 135–146.Google Scholar
Coughlan, G., Epstein, D., Sinha, A. & Honig, P. (2007). q-Forwards: Derivatives for Transferring Longevity and Mortality Risks. JPMorgan Pension Advisory Group, London.Google Scholar
Coughlan, G.D., Khalaf-Allah, M., Ye, Y., Kumar, S., Cairns, A.J., Blake, D. & Dowd, K. (2011). Longevity hedging 101. North American Actuarial Journal, 15(2), 150–176.10.1080/10920277.2011.10597615CrossRefGoogle Scholar
De Rosa, C., Luciano, E. & Regis, L. (2017). Basis risk in static versus dynamic longevity-risk hedging. Scandinavian Actuarial Journal, 2017(4), 343–365.CrossRefGoogle Scholar
Duan, J.-C. (2009). The GARCH Option Pricing Model Theory, Numerical Methods, Evidence and Applications. Risk Management Institute and Department of Finance National U of Singapore.Google Scholar
Engle, R.F. & Ng, V.K. (1993). Measuring and testing the impact of news on volatility. The Journal of Finance, 48(5), 1749.CrossRefGoogle Scholar
Engle, R.F. & Rosenberg, J.V. (1995). GARCH gamma. Journal of Derivarives, 2(4), 47–59.CrossRefGoogle Scholar
Fung, M.C., Peters, G.W. & Shevchenko, P.V. (2017). A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting. Annals of Actuarial Science, 11(02), 343–389.10.1017/S1748499517000069CrossRefGoogle Scholar
Gao, Q. & Hu, C. (2009). Dynamic mortality factor model with conditional heteroskedasticity. Insurance: Mathematics and Economics, 45(3), 410–423.Google Scholar
Giacometti, R., Bertocchi, M., Rachev, S.T. & Fabozzi, F.J. (2012). A comparison of the Lee-Carter model and AR-ARCH model for forecasting mortality rates. Insurance: Mathematics and Economics, 50(1), 85–93.Google Scholar
Glosten, L.R., Jagannathan, R. & Runkle, D.E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance, 48(5), 1779–1801.CrossRefGoogle Scholar
Koutmos, G. & Booth, G. (1995). Asymmetric volatility transmission in international stock markets. Journal of International Money and Finance, 14(6), 747–762.CrossRefGoogle Scholar
Lee, R. & Miller, T. (2001). Evaluating the performance of the Lee-Carter method for forecasting mortality. Demography, 38(4), 537–549.10.1353/dem.2001.0036CrossRefGoogle ScholarPubMed
Li, J.S.-H. & Hardy, M.R. (2011). Measuring basis risk in longevity hedges. North American Actuarial Journal, 15(2), 177–200.CrossRefGoogle Scholar
Lin, T., Wang, C.W. & Tsai, C.C.-L. (2015). Age-specific copula-AR-GARCH mortality models. Insurance: Mathematics and Economics, 61, 110–124.Google Scholar
Liu, Y. & Li, J.S.-H. (2016). The locally linear Cairns-Blake-Dowd model: a note on delta-nuga hedging of longevity risk. ASTIN Bulletin, 47(1), 79–151.CrossRefGoogle Scholar
Luciano, E. & Regis, L. (2014). Efficient versus inefficient hedging strategies in the presence of financial and longevity (value at) risk. Insurance: Mathematics and Economics, 55(1), 68–77.Google Scholar
Luciano, E., Regis, L. & Vigna, E. (2012). Delta-gamma hedging of mortality and interest rate risk. Insurance: Mathematics and Economics, 50(3), 402–412.Google Scholar
Luciano, E., Regis, L. & Vigna, E. (2017). Single- and cross-generation natural hedging of longevity and financial risk. Journal of Risk and Insurance, 84(3), 961–986.CrossRefGoogle Scholar
Michaelson, A. & Mulholland, J. (2014). Strategy for increasing the global capacity for longevity risk transfer: developing transactions that attract capital markets investors. The Journal of Alternative Investments, 17(1), 18–27.CrossRefGoogle Scholar
Nelson, D.B. (1991). Conditional heteroskedasticity in asset returns: a new approach. Econometrica, 59(2), 347.CrossRefGoogle Scholar
Wang, Z. & Li, J.S.-H. (2016). A DCC-GARCH multi-population mortality model and its applications to pricing catastrophic mortality bonds. Finance Research Letters, 16, 103–111.CrossRefGoogle Scholar
Zakoian, J.-M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18(5), 931–955.CrossRefGoogle Scholar
Zhou, K.Q. & Li, J.S.-H. (2017). Dynamic longevity hedging in the presence of population basis risk: a feasibility analysis from technical and economic perspectives. The Journal of Risk and Insurance, 84(S1), 417–437.CrossRefGoogle Scholar
Zhou, K.Q. & Li, J.S.-H. (2019a). Longevity Greeks: what do insurers and capital market investors need to know? North Americal Actuarial Journal, DOI: 10.1080/10920277.2019.1650283.CrossRefGoogle Scholar
Zhou, K.Q. & Li, J.S.-H. (2019b). Delta-hedging longevity risk under the M7–M5 model: the impact of cohort effect uncertainty and population basis risk. Insurance: Mathematics and Economics, 84, 1–21.Google Scholar