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

Author

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  • 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.

Suggested Citation

  • Michael McAleer & Juan-Angel Jimenez-Martin & Teodosio Perez-Amaral, 2009. "A Decision Rule to Minimize Daily Capital Charges in Forecasting Value-at-Risk," CIRJE F-Series CIRJE-F-644, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2009cf644
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    References listed on IDEAS

    as
    1. 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.
    2. Michael McAleer & Les Oxley, 2005. "The Ten Commandments for Academics," Journal of Economic Surveys, Wiley Blackwell, vol. 19(5), pages 823-826, December.
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    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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.
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    11. 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 245-269, July.
    12. 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.
    13. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    14. 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.
    15. 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.
    16. Michael McAleer, 2009. "The Ten Commandments For Optimizing Value-At-Risk And Daily Capital Charges," Journal of Economic Surveys, Wiley Blackwell, vol. 23(5), pages 831-849, December.
    17. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
    18. 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.
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    Citations

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    Cited by:

    1. Chia-Lin Chang & Michael Mcaleer, 2012. "Aggregation, Heterogeneous Autoregression And Volatility Of Daily International Tourist Arrivals And Exchange Rates," The Japanese Economic Review, Japanese Economic Association, vol. 63(3), pages 397-419, September.
    2. McAleer, Michael & Jimenez-Martin, Juan-Angel & Perez-Amaral, Teodosio, 2013. "GFC-robust risk management strategies under the Basel Accord," International Review of Economics & Finance, Elsevier, vol. 27(C), pages 97-111.
    3. Chia-Lin Chang & Michael Mcaleer, 2009. "Daily Tourist Arrivals, Exchange Rates and Voatility for Korea and Taiwan," Korean Economic Review, Korean Economic Association, vol. 25, pages 241-267.
    4. Hammoudeh, Shawkat & Malik, Farooq & McAleer, Michael, 2011. "Risk management of precious metals," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(4), pages 435-441.
    5. McAleer, Michael & Jimenez-Martin, Juan-Angel & Perez Amaral, Teodosio, 2009. "Optimal Risk Management Before, During and After the 2008-09 Financial Crisis," MPRA Paper 20975, University Library of Munich, Germany, revised 20 Sep 2009.
    6. Casarin, Roberto & Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & McAleer, Michael & Pérez-Amaral, Teodosio, 2013. "Risk management of risk under the Basel Accord: A Bayesian approach to forecasting Value-at-Risk of VIX futures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 183-204.
    7. Chia-lin Chang & Juan-Ángel Jiménez-Martín & Michael McAleer & Teodosio Pérez-Amaral, 2011. "Risk management of risk under the Basel Accord: forecasting value-at-risk of VIX futures," Managerial Finance, Emerald Group Publishing, vol. 37(11), pages 1088-1106, September.
    8. McAleer, Michael & Jimenez-Martin, Juan-Angel & Perez-Amaral, Teodosio, 2013. "Has the Basel Accord improved risk management during the global financial crisis?," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 250-265.
    9. Michael McAleer & Juan‐Ángel Jiménez‐Martín & Teodosio Pérez‐Amaral, 2013. "International Evidence on GFC‐Robust Forecasts for Risk Management under the Basel Accord," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(3), pages 267-288, April.
    10. Santos, André A.P. & Nogales, Francisco J. & Ruiz, Esther & Dijk, Dick Van, 2012. "Optimal portfolios with minimum capital requirements," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1928-1942.
    11. Jimenez-Martin, Juan-Angel & McAleer, Michael & Pérez-Amaral, Teodosio & Santos, Paulo Araújo, 2013. "GFC-robust risk management under the Basel Accord using extreme value methodologies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 223-237.
    12. Chang, Chia-Lin & Jiménez-Martín, Juan-Ángel & Maasoumi, Esfandiar & Pérez-Amaral, Teodosio, 2015. "A stochastic dominance approach to financial risk management strategies," Journal of Econometrics, Elsevier, vol. 187(2), pages 472-485.
    13. Michael McAleer, 2009. "The Ten Commandments For Optimizing Value-At-Risk And Daily Capital Charges," Journal of Economic Surveys, Wiley Blackwell, vol. 23(5), pages 831-849, December.
    14. Kaihua Deng, 2015. "Predicting By Learning: An Adaptive Rationale," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 1-14, December.
    15. Michael McAleer & Juan-Angel Jimenez-Martin & Teodosio Perez-Amaral, 2009. "What Happened to Risk Management During the 2008-09 Financial Crisis?," CARF F-Series CARF-F-155, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    16. Michael McAleer & Juan-Angel Jimenez-Martin & Teodosio Pérez-Amaral, 0000. "Has the Basel II Accord Encouraged Risk Management during the 2008-09 Financial Crisis?," Tinbergen Institute Discussion Papers 09-039/4, Tinbergen Institute.
    17. da Veiga, B. & Chan, F. & McAleer, M.J., 2009. "It Pays to Violate: How Effective are the Basel Accord Penalties?," Econometric Institute Research Papers EI 2009-39, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    18. Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Esfandiar Maasoumi & Michel McAleer & Teodosio Pérez-Amaral, 2015. "Choosing Expected Shortfall over VaR in Basel III Using Stochastic Dominance," Tinbergen Institute Discussion Papers 15-133/III, Tinbergen Institute.
    19. Juan-Ángel Jiménez-Martín & Michael McAleer & Teodosio Pérez-Amaral, 2009. "The Ten Commandments For Managing Value At Risk Under The Basel Ii Accord," Journal of Economic Surveys, Wiley Blackwell, vol. 23(5), pages 850-855, December.
    20. Sinha, Pankaj & Agnihotri, Shalini, 2014. "Sensitivity of Value at Risk estimation to NonNormality of returns and Market capitalization," MPRA Paper 56307, University Library of Munich, Germany, revised 26 May 2014.
    21. repec:eee:revfin:v:34:y:2017:i:c:p:86-98 is not listed on IDEAS

    More about this item

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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