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


McAleer, Michael and Jimenez-Martin, Juan-Angel and Pérez Amaral, Teodosio (2009) A Decision Rule to Minimize Daily Capital Charges in Forecasting Value-at-Risk. [ Documentos de trabajo del Instituto Complutense de Análisis Económico. ; nº 07, 2009, ] (Unpublished)


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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.

Item Type:Working Paper or Technical Report
Additional Information:

JEL Classifications: G32, G11, G17, C53.

Uncontrolled Keywords:Daily capital charges, Endogenous violations, Frequency of violations, Optimizing strategy, Risk forecasts, Value-at-risk.
Subjects:Social sciences > Economics > Finance
Sciences > Statistics > Mathematical statistics
Series Name:Documentos de trabajo del Instituto Complutense de Análisis Económico.
ID Code:8593

Basel Committee on Banking Supervision, (1988), International Convergence of Capital Measurement and Capital Standards, BIS, Basel, Switzerland.

Basel Committee on Banking Supervision, (1995), An Internal Model-Based Approach to Market Risk Capital Requirements, BIS, Basel, Switzerland.

Basel Committee on Banking Supervision, (1996), Supervisory Framework for the Use of “Backtesting” in Conjunction with the Internal Model-Based Approach to Market Risk Capital Requirements, BIS, Basel, Switzerland.

Berkowitz, J. and J. O'Brien (2001), How accurate are value-at-risk models at commercial banks?, Discussion Paper, Federal Reserve Board.

Bollerslev, T. (1986), Generalised autoregressive conditional heteroscedasticity, Journal of Econometrics, 31, 307-327.

Engle, R.F. (1982), Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1007.

Franses, P.H. and D. van Dijk (1999), Nonlinear Time Series Models in Empirical Finance, Cambridge, Cambridge University Press.

Gizycki, M. and N. Hereford (1998), Assessing the dispersion in banks’ estimates of market risk: the results of a value-at-risk survey, Discussion Paper 1, Australian Prudential Regulation Authority.

Glosten, L., R. Jagannathan and D. Runkle (1992), On the relation between the expected value and volatility of nominal excess return on stocks, Journal of Finance, 46, 1779-1801.

Jorion, P. (2000), Value at Risk: The New Benchmark for Managing Financial Risk, McGraw-Hill, New York.

Li, W.K., S. Ling and M. McAleer (2002), 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, 2002, pp. 9-33.

Ling, S. and M. McAleer (2002a), Stationarity and the existence of moments of a family of GARCH processes, Journal of Econometrics, 106, 109-117.

Ling, S. and M. McAleer (2002b), Necessary and sufficient moment conditions for the GARCH(r,s) and asymmetric power GARCH(r, s) models, Econometric Theory, 18, 722-729.

Ling, S. and M. McAleer, (2003a), Asymptotic theory for a vector ARMA-GARCH model, Econometric Theory, 19, 278-308.

Ling, S. and M. McAleer (2003b), On adaptive estimation in nonstationary ARMA models with GARCH errors, Annals of Statistics, 31, 642-674.

McAleer, M. (2005), Automated inference and learning in modeling financial volatility, Econometric Theory, 21, 232-261.

McAleer, M. (2008), The Ten Commandments for optimizing value-at-risk and daily capital charges, to appear in Journal of Economic Surveys.

McAleer, M., F. Chan and D. Marinova (2007), An econometric analysis of asymmetric volatility: theory and application to patents, Journal of Econometrics, 139, 259-284.

McAleer, M. and B. da Veiga (2008a), Forecasting value-at-risk with a parsimonious portfolio spillover GARCH (PS-GARCH) model, Journal of Forecasting, 27, 1-19.

McAleer, M. and B. da Veiga (2008b), Single index and portfolio models for forecasting value-at-risk thresholds, Journal of Forecasting, 27, 217-235.

Nelson, D.B. (1991), Conditional heteroscedasticity in asset returns: a new approach, Econometrica, 59, 347-370.

RiskmetricsTM (1996), J.P. Morgan Technical Document, 4th Edition, New York, J.P. Morgan.

Stahl, G. (1997), Three cheers, Risk, 10, 67-69.

Deposited On:09 Mar 2009 08:38
Last Modified:19 Jun 2015 09:22

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