Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-19T16:05:05.362Z Has data issue: false hasContentIssue false
  • English
  • Français

LOCAL HEDGING OF VARIABLE ANNUITIES IN THE PRESENCE OF BASIS RISK

Published online by Cambridge University Press:  25 April 2018

Denis-Alexandre Trottier ,
Frédéric Godin  and
Emmanuel Hamel
Denis-Alexandre Trottier
Affiliation:
Université Laval, Faculté des Sciences de l'Administration, Québec, Canada E-Mail: denis-alexandre.trottier.1@ulaval.ca
Frédéric Godin*
Affiliation:
Concordia University, Department of Mathematics and Statistics, Montréal, Québec, Canada, Université Laval, École d'Actuariat, Québec, Canada
Emmanuel Hamel
Affiliation:
Université Laval, École d'Actuariat, Québec, Canada E-Mail: emmanuel.hamel.1@ulaval.ca
*
E-Mail: frederic.godin@concordia.ca
Get access Rights & Permissions [Opens in a new window]

Abstract

A method to hedge variable annuities in the presence of basis risk is developed. A regime-switching model is considered for the dynamics of market assets. The approach is based on a local optimization of risk and is therefore very tractable and flexible. The local optimization criterion is itself optimized to minimize capital requirements associated with the variable annuity policy, the latter being quantified by the Conditional Value-at-Risk (CVaR) risk metric. In comparison to benchmarks, our method is successful in simultaneously reducing capital requirements and increasing profitability. Indeed the proposed local hedging scheme benefits from a higher exposure to equity risk and from time diversification of risk to earn excess return and facilitate the accumulation of capital. A robust version of the hedging strategies addressing model risk and parameter uncertainty is also provided.

Keywords

Basis riskhedgingsegregated fundsvariable annuitiesrisk measuresrisk managementregime-switching modelsG22G31G32C61
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 2 , May 2018 , pp. 611 - 646
Copyright
Copyright © Astin Bulletin 2018 

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

AAA (2011) The Application of C-3 Phase II and Actuarial Guideline XLIII. Variable Annuity Practice Note Work Group, American Academy of Actuaries. Available at: https://www.actuary.org/files/VAPN%20FINAL%20WEB%20040511.4.pdf/VAPN%20FINAL%20WEB%20040511.4.pdfGoogle Scholar
Ankirchner, S., Schneider, J.C. and Schweizer, N. (2014) Cross-hedging minimum return guarantees: Basis and liquidity risks. Journal of Economic Dynamics and Control, 41, 93–109.Google Scholar
Ardia, D., Kolly, J. and Trottier, D.-A. (2017) The impact of parameter and model uncertainty on market risk predictions from GARCH-type models. Journal of Forecasting, 36 (7), 808–823.Google Scholar
Artzner, P., Delbaen, F., Eber, J.M. and Heath, D. (1999) Coherent measures of risk. Mathematical Finance, 9 (3), 203–228.Google Scholar
Augustyniak, M. and Boudreault, M. (2012) An out-of-sample analysis of investment guarantees for equity-linked products: Lessons from the financial crisis of the late 2000s. North American Actuarial Journal, 16 (2), 183–206.Google Scholar
Augustyniak, M., Godin, F. and Simard, C. (2016) Assessing the effectiveness of local and global quadratic hedging under GARCH models. Quantitative Finance. 17 (9), 1305–1318.Google Scholar
Boudreault, M. and Augustyniak, M. (2015) On the importance of hedging dynamic lapses in variable annuities. Risk and Rewards, 66, 12–16.Google Scholar
Brandt, M.W. (2003) Hedging demands in hedging contingent claims. The Review of Economics and Statistics, 85 (1), 119–140.CrossRefGoogle Scholar
Chopra, D., Erzan, O., de Gantès, G., Grepin, L. and Slawner, C. (2009) Responding to the variable annuity crisis. Mckinsey Working Papers on Risk.Google Scholar
CIA (2010) Mortality Improvement Research Paper. Document 210065, Canadian Institute of Actuaries. Available at: http://www.cia-ica.ca/docs/default-source/2010/210065e.pdfGoogle Scholar
CIA (2014). Document 214013, Canadian Institute of Actuaries.Available at: http://www.cia-ica.ca/docs/default-source/2014/214013e.pdf Final Report: Canadian Pensioners MortalityGoogle Scholar
Ederington, L.H. (1979) The hedging performance of the new futures markets. The Journal of Finance, 34 (1), 157–170.Google Scholar
Elliott, R.J., Chan, L. and Siu, T.K. (2005) Option pricing and esscher transform under regime switching. Annals of Finance, 1 (4), 423–432.Google Scholar
François, P., Gauthier, G. and Godin, F. (2014) Optimal hedging when the underlying asset follows a regime-switching Markov process. European Journal of Operational Research, 237 (1), 312–322.CrossRefGoogle Scholar
Gaillardetz, P., Li, H. Y. and MacKay, A. (2012) Equity-linked products: Evaluation of the dynamic hedging errors under stochastic mortality. European Actuarial Journal, 2 (2), 243–258.Google Scholar
Godin, F. (2016) Minimizing CVaR in global dynamic hedging with transaction costs. Quantitative Finance, 16 (3), 461–475.Google Scholar
Hamilton, J.D. (1989) A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57 (2), 357–384.Google Scholar
Hardy, M.R. (2001) A regime-switching model of long-term stock returns. North American Actuarial Journal, 5 (2), 41–53.CrossRefGoogle Scholar
Hardy, M.R. (2003) Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance. Hoboken, NJ: John Wiley & Sons.Google Scholar
iA Financial Group (2016) 2015 Annual report. Available at: https://files.ia.ca/-/media/files/ia/investisseurs/rapportsfinanciers/annuel/2016/en/annual_documents/da-2015-annual-report-secured.pdfGoogle Scholar
Kling, A., Ruez, F. and Ruß, J. (2014) The impact of policyholder behavior on pricing, hedging, and hedge efficiency of withdrawal benefit guarantees in variable annuities. European Actuarial Journal, 4 (2), 281–314.Google Scholar
Ledlie, M.C., Corry, D.P., Finkelstein, G.S., Ritchie, A.J., Su, K. and Wilson, D.C.E. (2008) Variable annuities. British Actuarial Journal, 14 (2), 327–389.Google Scholar
MacKay, A., Augustyniak, M., Bernard, C. and Hardy, M.R. (2017) Risk management of policyholder behavior in equity-linked life insurance. Journal of Risk and Insurance, 84 (2), 661–690.Google Scholar
Manulife Financial Corporation (2016) 2015 Annual report.Available at: http://www.manulife.com/servlet/servlet.FileDownload?file=00P5000000dfLKVEA2Google Scholar
Qian, L., Yang, H. and Wang, R. (2011) Locally risk-minimizing hedging strategies for unit-linked life insurance contracts under a regime switching lévy model. Frontiers of Mathematics in China, 6 (6), 1185–1202.Google Scholar
Robidoux, B. (2015) Introduction to predictive modeling of fund manager behavior for variable annuities riders. Predictive Analytics and Futurism, 12, 24–26.Google Scholar
Rockafellar, R.T. and Uryasev, S. (2000) Optimization of conditional value-at-risk. Journal of Risk, 2, 21–42.CrossRefGoogle Scholar
Rockafellar, R.T. and Uryasev, S. (2002) Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 26 (7), 1443–1471.Google Scholar
Rockafellar, R.T., Uryasev, S.P. and Zabarankin, M. (2002) Deviation measures in risk analysis and optimization. Working paper, University of Florida.Google Scholar
Wang, S.S. (2000) A class of distortion operators for pricing financial and insurance risks. The Journal of Risk and Insurance, 67 (1), 15–36.Google Scholar
Wang, Y. and Yin, G. (2012) Quantile hedging for guaranteed minimum death benefits with regime switching. Stochastic Analysis and Applications, 30 (5), 799–826.Google Scholar
Zhang, F. (2010) Integrating robust risk management into pricing: New thinking for VA writers. Risk and Rewards, 55, 34–36.Google Scholar
Zhang, J., Tan, K.S. and Weng, C. (2017) Optimal hedging with basis risk under mean–variance criterion. Insurance: Mathematics and Economics, 75, 1–15.Google Scholar