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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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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. 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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File URL: http://eprints.ucm.es/13218/1/1132.pdf
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Bibliographic Info

Paper provided by Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales in its series Documentos del Instituto Complutense de Análisis Económico with number 2011-32.

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Length: 46 pages
Date of creation: 2011
Date of revision:
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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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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  1. 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.
  2. Michael McAleer, 2009. "The Ten Commandments for Optimizing Value-at-Risk and Daily Capital Charges," Documentos del Instituto Complutense de Análisis Económico 0910, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
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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," Tinbergen Institute Discussion Papers 13-085/III, Tinbergen Institute, revised 08 Jul 2013.
  2. 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.
  3. Chia-Lin Chang & Juan-Angel Jimenez-Martin & Michael McAleer & Teodosio Pérez-Amaral, 2011. "The Rise and Fall of S&P500 Variance Futures," Documentos del Instituto Complutense de Análisis Económico 2011-35, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.

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