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

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Author Info

  • Michael McAleer

    (Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute and Center for International Research on the Japanese Economy (CIRJE), Faculty of Economics, University of Tokyo)

  • Juan-Angel Jimenez-Martin

    (Department of Quantitative Economics, Complutense University of Madrid)

  • Teodosio Perez-Amaral

    (Department of Quantitative Economics, Complutense University of Madrid)

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 analyze the profit maximizing problem of an ADI subject to capital requirements under the Basel II Accord as ADI's have to choose an optimal VaR reporting strategy that minimizes daily capital charges. Accordingly, we suggest a dynamic communication and forecasting strategy 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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File URL: http://www.carf.e.u-tokyo.ac.jp/pdf/workingpaper/fseries/164.pdf
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Bibliographic Info

Paper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-159.

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Length: 36 pages
Date of creation: Aug 2009
Date of revision:
Handle: RePEc:cfi:fseres:cf159

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  1. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University.
  2. 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.
  3. Topaloglu, Huseyin, 2009. "A tighter variant of Jensen's lower bound for stochastic programs and separable approximations to recourse functions," European Journal of Operational Research, Elsevier, vol. 199(2), pages 315-322, December.
  4. 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.
  5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  6. 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.
  7. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  8. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. Li, W K & Ling, Shiqing & McAleer, Michael, 2002. " Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 245-69, July.
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