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Risk Management of Risk Under the Basel Accord: A Bayesian Approach to Forecasting Value-at-Risk of VIX Futures

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  • Michael McAleer

    (Erasmus University Rotterdam, Tinbergen Institute, The Netherlands, Complutense University of Madrid, and Institute of Economic Research, Kyoto University)

  • Roberto Casarin

    (Department of Economics Ca’Foscari University of Venice)

  • Chia-Lin Chang

    (Department of Applied Economics Department of Finance National Chung Hsing University Taichung, Taiwan)

  • Juan-Ángel Jiménez-Martín

    (Department of Quantitative Economics Complutense University of Madrid)

  • Teodosio Pérez-Amaral

    (Department of Quantitative Economics Complutense University of Madrid)

Abstract

It is well known that the Basel II Accord requires banks and other Authorized Deposit-taking Institutions (ADIs) to communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one or more risk models, whether individually or as combinations, 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 et al. (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, and extends the approaches given in McAleer et al. (2009) and Chang et al. (2011) to examine how different risk management strategies performed during the 2008-09 global financial crisis (GFC). The empirical results suggest that an aggressive strategy of choosing the Supremum of single model forecasts, as compared with Bayesian and non-Bayesian combinations of models, is preferred to other alternatives, and is robust during the GFC. However, this strategy implies relatively high numbers of violations and accumulated losses, which are admissible under the Basel II Accord.

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Bibliographic Info

Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 784.

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Date of creation: Jul 2011
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Handle: RePEc:kyo:wpaper:784

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Keywords: Median strategy; Value-at-Risk; daily capital charges; violation penalties; aggressive risk management; conservative risk management; Basel Accord; VIX futures; Bayesian strategy; quantiles; forecast densities.;

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References

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  1. Michael McAleer & Juan-Angel Jimenez-Martin & Teodosio Perez-Amaral, 2009. "A Decision Rule to Minimize Daily Capital Charges in Forecasting Value-at-Risk," CARF F-Series CARF-F-159, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  2. Casarin, R. & Chang, C-L. & Jimenez-Martin, J-A. & McAleer, M.J. & Perez-Amaral, T., 2011. "Risk Management of Risk Under the Basel Accord: A Bayesian Approach to Forecasting Value-at-Risk of VIX Futures," Econometric Institute Research Papers EI2011-29, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  3. Michael McAleer & Juan-Ángel Jiménez-Martín & Teodosio Pérez-Amaral, 2010. "GFC-Robust Risk Management Strategies under the Basel Accord," KIER Working Papers 727, Kyoto University, Institute of Economic Research.
  4. 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.
  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. Monica Billio & Roberto Casarin & Francesco Ravazzolo & Herman K. van Dijk, 2010. "Combining predictive densities using Bayesian filtering with applications to US economics data," Working Paper 2010/29, Norges Bank.
  7. Michael McAleer & Juan-Ángel Jiménez-Martín & Teodosio Pérez-Amaral, 2011. "International Evidence on GFC-robust Forecasts for Risk Management under the Basel Accord," Working Papers in Economics 11/05, University of Canterbury, Department of Economics and Finance.
  8. 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.
  9. 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.
  10. 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.
  11. Jose A. Lopez, 1998. "Methods for evaluating value-at-risk estimates," Economic Policy Review, Federal Reserve Bank of New York, issue Oct, pages 119-124.
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  13. 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.
  14. Michael McAleer & Juan-Ángel Jiménez-Martín & Teodosio Pérez-Amaral, 2011. "Has the Basel II Accord Encouraged Risk Management During the 2008-09 Financial Crisis?," KIER Working Papers 767, Kyoto University, Institute of Economic Research.
  15. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
  16. Caporin, M. & McAleer, M.J., 2010. "Model Selection and Testing of Conditional and Stochastic Volatility Models," Econometric Institute Research Papers EI 2010-57, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  17. Shiqing Ling & Michael McAleer, 2001. "Stationarity and the Existence of Moments of a Family of GARCH Processes," ISER Discussion Paper 0535, Institute of Social and Economic Research, Osaka University.
  18. 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.
  19. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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  22. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  23. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University.
  24. Shiqing Ling & Michael McAleer, 2001. "Necessary and Sufficient Moment Conditions for the GARCH(r,s) and Asymmetric Power GARCH(r,s) Models," ISER Discussion Paper 0534, Institute of Social and Economic Research, Osaka University.
  25. 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.
  26. 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.
  27. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
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Cited by:
  1. Chia-Lin Chang & David E. Allen & Michael McAleer & Teodosio Perez Amaral, 2013. "Risk Modelling and Management: An Overview," KIER Working Papers 872, Kyoto University, Institute of Economic Research.
  2. Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & McAleer, Michael & Amaral, Teodosio Perez, 2013. "The rise and fall of S&P500 variance futures," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 151-167.
  3. Michael McAleer & Roberto Casarin & Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Teodosio Pérez-Amaral, 2011. "Risk Management of Risk Under the Basel Accord: A Bayesian Approach to Forecasting Value-at-Risk of VIX Futures," KIER Working Papers 784, Kyoto University, Institute of Economic Research.

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