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Risk Management of Risk under the Basel Accord: Forecasting Value-at-Risk of VIX Futures

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  • Chia-Lin Chang
  • Juan-Ángel Jiménez-Martín
  • Michael McAleer

    ()
    (University of Canterbury)

  • Teodosio Pérez-Amaral

Abstract

The Basel II Accord requires that banks and other Authorized Deposit-taking Institutions (ADIs) communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one or more risk models to measure Value-at-Risk (VaR). The risk estimates of these models are used to determine capital requirements and associated capital costs of ADIs, depending in part on the number of previous violations, whereby realised losses exceed the estimated VaR. McAleer, Jimenez-Martin and Perez-Amaral (2009) proposed a new approach to model selection for predicting VaR, consisting of combining alternative risk models, and comparing conservative and aggressive strategies for choosing between VaR models. This paper addresses the question of risk management of risk, namely VaR of VIX futures prices. We examine how different risk management strategies performed during the 2008-09 global financial crisis (GFC). We find that an aggressive strategy of choosing the Supremum of the single model forecasts is preferred to the other alternatives, and is robust during the GFC. However, this strategy implies relatively high numbers of violations and accumulated losses, though these are admissible under the Basel II Accord.

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File URL: http://www.econ.canterbury.ac.nz/RePEc/cbt/econwp/1112.pdf
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Bibliographic Info

Paper provided by University of Canterbury, Department of Economics and Finance in its series Working Papers in Economics with number 11/12.

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Length: 31 pages
Date of creation: 01 Feb 2011
Date of revision:
Handle: RePEc:cbt:econwp:11/12

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Keywords: Median strategy; Value-at-Risk (VaR); daily capital charges; violation penalties; optimizing strategy; aggressive risk management; conservative risk management; Basel II Accord; VIX futures; global financial crisis (GFC);

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References

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  1. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
  2. Michael McAleer & Juan‐Ángel Jiménez‐Martín & Teodosio Pérez‐Amaral, 2013. "International Evidence on GFC‐Robust Forecasts for Risk Management under the Basel Accord," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(3), pages 267-288, 04.
  3. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  4. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  5. Juan-�ngel Jiménez-Martín & Michael McAleer & Teodosio Pérez-Amaral, 2009. "The Ten Commandments For Managing Value At Risk Under The Basel Ii Accord," Journal of Economic Surveys, Wiley Blackwell, vol. 23(5), pages 850-855, December.
  6. McAleer, Michael & Wiphatthanananthakul, Chatayan, 2010. "A simple expected volatility (SEV) index: Application to SET50 index options," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2079-2090.
  7. Li, W K & Ling, Shiqing & McAleer, Michael, 2002. " Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 245-69, July.
  8. McAleer, Michael & Chan, Felix & Marinova, Dora, 2007. "An econometric analysis of asymmetric volatility: Theory and application to patents," Journal of Econometrics, Elsevier, vol. 139(2), pages 259-284, August.
  9. Shiqing Ling & Michael McAleer, 2001. "On Adaptive Estimation in Nonstationary ARMA Models with GARCH Errors," ISER Discussion Paper 0548, Institute of Social and Economic Research, Osaka University.
  10. Michael McAleer & Bernardo da Veiga, 2008. "Single-index and portfolio models for forecasting value-at-risk thresholds," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(3), pages 217-235.
  11. McAleer, M.J. & Jimenez-Martin, J-A. & Perez-Amaral, T., 2010. "GFC-Robust Risk Management Strategies under the Basel Accord," Econometric Institute Research Papers EI 2010-59, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  12. Michael McAleer & Juan-Angel Jimenez-Martin & Teodosio Perez-Amaral, 2009. "A Decision Rule to Minimize Daily Capital Charges in Forecasting Value-at-Risk," CIRJE F-Series CIRJE-F-644, CIRJE, Faculty of Economics, University of Tokyo.
  13. Michael Mcaleer & Bernardo da Veiga, 2008. "Forecasting value-at-risk with a parsimonious portfolio spillover GARCH (PS-GARCH) model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(1), pages 1-19.
  14. Michael McAleer, 2009. "The Ten Commandments for Optimizing Value-at-Risk and Daily Capital Charges," CIRJE F-Series CIRJE-F-652, CIRJE, Faculty of Economics, University of Tokyo.
  15. Michael McAleer & Juan-Angel Jimenez-Martin & Teodosio P�rez-Amaral, 0000. "Has the Basel II Accord Encouraged Risk Management During the 2008-09 Financial Crisis?," Tinbergen Institute Discussion Papers 09-039/4, Tinbergen Institute.
  16. Massimiliano Caporin & Michael McAleer, 2010. "Model Selection and Testing of Conditional and Stochastic Volatility Models," Working Papers in Economics 10/58, University of Canterbury, Department of Economics and Finance.
  17. Pérignon, Christophe & Deng, Zi Yin & Wang, Zhi Jun, 2008. "Do banks overstate their Value-at-Risk?," Journal of Banking & Finance, Elsevier, vol. 32(5), pages 783-794, May.
  18. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April.
  19. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(03), pages 722-729, June.
  20. Massimiliano Caporin & Michael McAleer, 2010. "The Ten Commandments For Managing Investments," Journal of Economic Surveys, Wiley Blackwell, vol. 24(1), pages 196-200, 02.
  21. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  22. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
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Cited by:
  1. Roberto Casarin & Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Michael McAleer & Teodosio Pérez Amaral, 2011. "Risk Management of Risk Under the Basel Accord: A Bayesian Approach to Forecasting Value-at-Risk of VIX Futures," Documentos de Trabajo del ICAE 2011-32, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  2. Chang, C-L. & Jimenez-Martin, J-A. & McAleer, M.J. & Perez-Amaral, T., 2011. "The Rise and Fall of S&P500 Variance Futures," Econometric Institute Research Papers EI2011-37, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  3. Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Esfandiar Maasoumi & Teodosio Pérez Amaral, 2014. "A Stochastic Dominance Approach to Financial Risk Management Strategies," Documentos de Trabajo del ICAE 2014-08, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Apr 2014.

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