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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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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. Previous papers 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, using Bayesian and non- Bayesian combinations of models addresses the question of risk management of risk, namely VaR of VIX futures prices, and extends the approaches given in previous papers to examine how different risk management strategies performed during the 2008-09 global financial crisis (GFC). The use of time-varying weights using Bayesian methods, allows dynamic combinations of the different models to obtain a more accurate VaR forecasts than the estimates and forecasts that might be produced by a single model of risk. One of these dynamic combinations are endogenously determined by the pass performance in terms of daily capital charges of the individual models. This can improve the strategies to minimize daily capital charges, which is a central objective of ADIs. 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.

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  • 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.
  • Handle: RePEc:ucm:doicae:1132 Note: The authors are most grateful for the helpful comments and suggestions of participants at the Kansai Econometrics Conference, Osaka, Japan, January 2011, and the International Conference on Risk Modelling and Management, Madrid, Spain, June 2011. For financial support, the second author acknowledges the National Science Council, Taiwan, the third and fifth authors acknowledge the Ministerio de Ciencia y Tecnología and Comunidad de Madrid, Spain, and the fourth author wishes to thank the Australian Research Council, National Science Council, Taiwan, and the Japan Society for the Promotion of Science.
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    1. repec:eee:eneeco:v:66:y:2017:i:c:p:194-204 is not listed on IDEAS
    2. Casarin, Roberto & Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & McAleer, Michael & Pérez-Amaral, Teodosio, 2013. "Risk management of risk under the Basel Accord: A Bayesian approach to forecasting Value-at-Risk of VIX futures," Mathematics and Computers in Simulation (MATCOM), Elsevier, pages 183-204.
    3. Cadsby, C. Bram & Servátka, Maroš & Song, Fei, 2013. "How competitive are female professionals? A tale of identity conflict," Journal of Economic Behavior & Organization, Elsevier, vol. 92(C), pages 284-303.
    4. Casarin, Roberto & Grassi, Stefano & Ravazzolo, Francesco & van Dijk, Herman K., 2015. "Parallel Sequential Monte Carlo for Efficient Density Combination: The DeCo MATLAB Toolbox," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(i03).
    5. 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.
    6. Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Esfandiar Maasoumi & Michael McAleer & Teodosio Pérez-Amaral, 2015. "A Stochastic Dominance Approach to the Basel III Dilemma: Expected Shortfall or VaR?," Documentos de Trabajo del ICAE 2015-16, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    7. Chia-Lin Chang & David E. Allen & Michael McAleer & Ju-Ting Tang & Teodosio Pérez Amaral, 2013. "Risk Modelling and Management: An Overview," Documentos de Trabajo del ICAE 2013-22, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    8. Tim Leung & Brian Ward, 2015. "The golden target: analyzing the tracking performance of leveraged gold ETFs," Studies in Economics and Finance, Emerald Group Publishing, vol. 32(3), pages 278-297, August.
    9. repec:eee:empfin:v:42:y:2017:i:c:p:175-198 is not listed on IDEAS
    10. Casarin, Roberto & Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & McAleer, Michael & Pérez-Amaral, Teodosio, 2013. "Risk management of risk under the Basel Accord: A Bayesian approach to forecasting Value-at-Risk of VIX futures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 183-204.
    11. Richard Gerlach & Chao Wang, 2016. "Bayesian Semi-parametric Realized-CARE Models for Tail Risk Forecasting Incorporating Realized Measures," Papers 1612.08488, arXiv.org.
    12. Chang, Chia-Lin & Jiménez-Martín, Juan-Ángel & Maasoumi, Esfandiar & Pérez-Amaral, Teodosio, 2015. "A stochastic dominance approach to financial risk management strategies," Journal of Econometrics, Elsevier, vol. 187(2), pages 472-485.
    13. Chao Wang & Qian Chen & Richard Gerlach, 2017. "Bayesian Realized-GARCH Models for Financial Tail Risk Forecasting Incorporating Two-sided Weibull Distribution," Papers 1707.03715, arXiv.org.

    More about this item

    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.;

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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