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A Decision Rule to Minimize Daily Capital Charges in Forecasting Value-at-Risk

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Author Info
Juan Angel Jiménez Martín () (Universidad Complutense de Madrid. Facultad de CC. Económicas y Empresariales. Dpto. de Fundamentos de Análisis Económico II.)
Michael McAleer (Department of Quantitative Economics Complutense University of Madrid and Econometric Institute Erasmus University Rotterdam)
Teodosio Pérez-Amaral (Department of Quantitative Economics Complutense University of Madrid)

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Abstract

Under the Basel II Accord, banks and other Authorized Deposit-taking Institutions (ADIs) have to communicate their daily risk estimates to the monetary authorities at the beginning of the trading day, using a variety of Value-at-Risk (VaR) models to measure risk. Sometimes the risk estimates communicated using these models are too high, thereby leading to large capital requirements and high capital costs. At other times, the risk estimates are too low, leading to excessive violations, so that realised losses are above the estimated risk. In this paper we propose a learning strategy that complements existing methods for calculating VaR and lowers daily capital requirements, while restricting the number of endogenous violations within the Basel II Accord penalty limits. We suggest a decision rule that responds to violations in a discrete and instantaneous manner, while adapting more slowly in periods of no violations. We apply the proposed strategy to Standard & Poor’s 500 Index and show there can be substantial savings in daily capital charges, while restricting the number of violations to within the Basel II penalty limits.

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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 0907.

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Date of creation: 2009
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Handle: RePEc:ucm:doicae:0907

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  1. 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. [Downloadable!] (restricted)
  2. Benjaafar, Saifallah & Morin, Thomas L. & Talavage, Joseph J., 1995. "The strategic value of flexibility in sequential decision making," European Journal of Operational Research, Elsevier, vol. 82(3), pages 438-457, May. [Downloadable!] (restricted)
  3. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(03), pages 722-729, June. [Downloadable!]
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  4. 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. [Downloadable!]
  5. 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. [Downloadable!]
  6. 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. [Downloadable!]
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  7. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April. [Downloadable!]
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  8. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January. [Downloadable!] (restricted)
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  9. Li, W K & Ling, Shiqing & McAleer, Michael, 2002. " Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Blackwell Publishing, vol. 16(3), pages 245-69, July. [Downloadable!] (restricted)
  10. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February. [Downloadable!]
  11. Susan Thomas & Mandira Sarma & Ajay Shah, 2003. "Selection of Value-at-Risk models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(4), pages 337-358. [Downloadable!]
  12. 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. [Downloadable!]
  13. Andris Möller & Werner Römisch & Klaus Weber, 2008. "Airline network revenue management by multistage stochastic programming," Computational Management Science, Springer, vol. 5(4), pages 355-377, October. [Downloadable!] (restricted)
  14. 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. [Downloadable!] (restricted)
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  1. Michael McAleer & Juan-Angel Jimenez-Martin & Teodosio Pérez-Amaral, . "Has the Basel II Accord Encouraged Risk Management During the 2008-09 Financial Crisis?," Tinbergen Institute Discussion Papers 09-039/4, Tinbergen Institute. [Downloadable!]
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