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

Casarin, Roberto and Chang, Chia-Lin and Jiménez Martín, Juan Ángel and McAleer, Michael and Pérez Amaral, Teodosio (2011) Risk Management of Risk Under the Basel Accord: A Bayesian Approach to Forecasting Value-at-Risk of VIX Futures. [Working Paper or Technical Report] (Unpublished)

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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.

Item Type:Working Paper or Technical Report
Additional Information:JEL Classifications: G32, G17, C53, C22, C11. 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.
Uncontrolled 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.
Subjects:Social sciences > Economics > Econometrics
Series Name:Documentos de Trabajo del Instituto Complutense de Análisis Económico
Volume:2011
Number:32
ID Code:13218
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Last Modified:15 Nov 2013 10:49

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