Risk Management of Risk Under the Basel AccordA Bayesian Approach to Forecasting Value-at-Risk of VIX Futures

  1. Casarin, Roberto
  2. Chang, Chia-Lin
  3. Jiménez-Martín, Juan-Ángel
  4. McAleer, Michael
  5. Pérez Amaral, Teodosio
Revista:
Documentos de Trabajo (ICAE)

ISSN: 2341-2356

Año de publicación: 2011

Número: 32

Páginas: 1-46

Tipo: Documento de Trabajo

DIALNET GOOGLE SCHOLAR lock_openDocta Complutense editor

Otras publicaciones en: Documentos de Trabajo (ICAE)

Resumen

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.

Referencias bibliográficas

  • A. Doucet, J.G. Freitas and J. Gordon, Sequential Monte Carlo Methods in Practice, Springer Verlag, New York, 2001.
  • B. Huskaj, A value-at-risk analysis of VIX futures long memory, heavy tails, and asymmetry. Available at SSRN: http://ssrn.com/abstract=1495229, 2009.
  • Basel Committee on Banking Supervision, An Internal Model-Based Approach to Market Risk Capital Requirements, BIS, Basel, Switzerland, 1995.
  • Basel Committee on Banking Supervision, International Convergence of Capital Measurement and Capital Standards, BIS, Basel, Switzerland, 1988.
  • Basel Committee on Banking Supervision, International Convergence of Capital Measurement and Capital Standards, A Revised Framework Comprehensive Version, BIS, Basel, Switzerland, 2006.
  • Basel Committee on Banking Supervision, Supervisory Framework for the Use of “Backtesting” in Conjunction with the Internal Model-Based Approach to Market Risk Capital Requirements, BIS, Basel, Switzerland, 1996.
  • C. Borio, The financial turmoil of 2007-?: A preliminary assessment and some policy considerations, BIS Working Papers No 251, Bank for International Settlements, Basel, Switzerland, 2008.
  • C. Pérignon, Z.-Y. Deng and Z.-J. Wang, Do banks overstate their value-at-risk?, Journal of Banking & Finance, 32 (2008) 783-794.
  • C.-L. Chang, J-A. Jimenez-Martin, M. McAleer and T. Perez Amaral, Risk management of risk under the Basel Accord: Forecasting value-at-risk of VIX futures, to appear in Managerial Finance (Available at SSRN: http://ssrn.com/abstract=1765202), 2011.
  • Chicago Board Options Exchange, VIX: CBOE volatility index, Working paper, Chicago, 2003.
  • D. B. Nelson, Conditional heteroscedasticity in asset returns: A new approach, Econometrica, 59 (1991) 347-370.
  • F. Black, Studies of stock market volatility changes, in 1976 Proceedings of the American Statistical Association, Business & Economic Statistics Section, (1976) 177-181.
  • G. Stahl, Three cheers, Risk, 10 (1997) 67-69.
  • G. Zumbach, A Gentle Introduction to the RM 2006 Methodology, New York, Riskmetrics Group, 2007.
  • J. Berkowitz, and J. O’Brien, How accurate are value-at-risk models at commercial banks?, Discussion Paper, Federal Reserve Board, 2001.
  • J.-A. Jimenez-Martin, McAleer, M. and T. Pérez-Amaral, The Ten Commandments for managing value-at-risk under the Basel II Accord, Journal of Economic Surveys, 23, (2009) 850-855.
  • J.A. Lopez, Methods for evaluating value-at-risk estimates, Economic Review, Federal Reserve Bank of San Francisco, 3-17, 1999.
  • L. Glosten, R. Jagannathan and D. Runkle, On the relation between the expected value and volatility of nominal excess return on stocks, Journal of Finance, 46 (1992) 1779- 1801.
  • Li, W.K., S. Ling and M. McAleer, Recent theoretical results for time series models with GARCH errors, Journal of Economic Surveys, 16, 245-269. Reprinted in M. McAleer and L. Oxley (eds.), Contributions to Financial Econometrics: Theoretical and Practical Issues, Blackwell, Oxford, 9-33, 2002.
  • M. Billio, R. Casarin, F. Ravazzolo and H.K. van Dijk, Combining predictive densities using Bayesian filtering with applications to US economics data, Norges Bank Working Paper No. 2010/29, 2010.
  • M. Caporin, and M. McAleer, Model selection and testing of conditional and stochastic volatility models, to appear in L. Bauwens, C. Hafner and S. Laurent (eds.), Handbook on Financial Engineering and Econometrics: Volatility Models and Their Applications, Wiley, New York (Available at SSRN: http://ssrn.com/abstract=1676826), 2010b.
  • M. Caporin, and M. McAleer, The Ten Commandments for managing investments, Journal of Economic Surveys, 24 (2010a) 196-200.
  • M. Gizycki, and N. Hereford, Assessing the dispersion in banks’ estimates of market risk: the results of a value-at-risk survey, Discussion Paper 1, Australian Prudential Regulation Authority, 1998.
  • M. McAleer and B. da Veiga, Forecasting value-at-risk with a parsimonious portfolio spillover GARCH (PS-GARCH) model, Journal of Forecasting, 27 (2008a) 1-19.
  • M. McAleer and B. da Veiga, Single index and portfolio models for forecasting value-atrisk thresholds, Journal of Forecasting, 27 (2008b) 217-235.
  • M. McAleer and C. Wiphatthanananthakul, A simple expected volatility (SEV) index: Application to SET50 index options, Mathematics and Computers in Simulation, 80 (2010) 2079-2090.
  • M. McAleer, Automated inference and learning in modeling financial volatility, Econometric Theory, 21 (2005) 232-261.
  • M. McAleer, F. Chan and D. Marinova, An econometric analysis of asymmetric volatility: theory and application to patents, Journal of Econometrics, 139 (2007) 259- 284.
  • M. McAleer, J.-Á. Jiménez-Martin and T. Pérez-Amaral, A decision rule to minimize daily capital charges in forecasting value-at-risk, Journal of Forecasting, 29 (2010a) 617-634.
  • M. McAleer, J.-Á. Jiménez-Martin and T. Pérez-Amaral, GFC-robust risk management strategies under the Basel Accord, Available at SSRN: http://ssrn.com/abstract=1688385, 2010c.
  • M. McAleer, J.-Á. Jiménez-Martin and T. Pérez-Amaral, Has the Basel II Accord encouraged risk management during the 2008-09 financial crisis?, Available at SSRN: http://ssrn.com/abstract=1397239, 2010b.
  • M. McAleer, J.-Á. Jiménez-Martin and T. Pérez-Amaral, International evidence on GFCrobust forecasts for risk management under the Basel Accord. Available at SSRN: http://ssrn.com/abstract=1741565, 2011.
  • M. McAleer, The Ten Commandments for optimizing value-at-risk and daily capital charges, Journal of Economic Surveys, 23 (2009) 831-849.
  • N. Shephard, Statistical aspects of ARCH and stochastic volatility, in O.E. BarndorffNielsen, D.R. Cox and D.V. Hinkley (eds.), Statistical Models in Econometrics, Finance and Other Fields, Chapman & Hall, London, 1-67, 1996.
  • P. Jorion, Value at Risk: The New Benchmark for Managing Financial Risk, McGrawHill, New York, 2000.
  • P.H. Franses, and D. van Dijk, Nonlinear Time Series Models in Empirical Finance, Cambridge, Cambridge University Press, 1999.
  • R.F. Engle, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50 (1982) 987-1007.
  • RE. Whaley, Derivatives on market volatility: Hedging tools long overdue, Journal of Derivatives, 1 (1993) 71-84.
  • Riskmetrics, J.P. Morgan Technical Document, 4th Edition, New York, J.P. Morgan, 1996.
  • S. Ling, and M. McAleer, Asymptotic theory for a vector ARMA-GARCH model, Econometric Theory, 19 (2003a) 278-308.
  • S. Ling, and M. McAleer, Necessary and sufficient moment conditions for the GARCH(r,s) and asymmetric power GARCH(r,s) models, Econometric Theory, 18 (2002b) 722-729.
  • S. Ling, and M. McAleer, On adaptive estimation in nonstationary ARMA models with GARCH errors, Annals of Statistics, 31(2003b) 642-674.
  • S. Ling, and M. McAleer, Stationarity and the existence of moments of a family of GARCH processes, Journal of Econometrics, 106 (2002a) 109-117. T. Bollerslev, Generalised autoregressive conditional heteroscedasticity, Journal of Econometrics, 31 (1986) 307-327.
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