A decision rule to minimize daily capital charges in forecasting value-at-risk

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 realized 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 ADIs 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. Copyright © 2009 John Wiley & Sons, Ltd.

[1]  Saifallah Benjaafar,et al.  The strategic value of flexibility in sequential decision making , 1995 .

[2]  Daniel B. Nelson.  CONDITIONAL HETEROSKEDASTICITY IN ASSET RETURNS: A NEW APPROACH , 1991 .

[3]  Keisuke Hirano,et al.  Decision Theory in Econometrics , 2010 .

[4]  Robert J. Vanderbei,et al.  Robust Optimization of Large-Scale Systems , 1995, Oper. Res..

[5]  Jeremy Berkowitz,et al.  How accurate are Value-at-Risk models at commercial banks? , 2001 .

[6]  Phhilippe Jorion.  Value at Risk: The New Benchmark for Managing Financial Risk , 2000 .

[7]  Michael McAleer,et al.  NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS , 2002, Econometric Theory.

[8]  Michael McAleer,et al.  Forecasting value‐at‐risk with a parsimonious portfolio spillover GARCH (PS‐GARCH) model , 2008 .

[9]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[10]  Susan Thomas,et al.  Selection of Value-at-Risk models , 2003 .

[11]  M. McAleer,et al.  Stationarity and the existence of moments of a family of GARCH processes , 2002 .

[12]  Jeremy Berkowitz,et al.  How Accurate are Value-at-Risk Models at Commercial Banks , 2001 .

[13]  M. McAleer.  Automated Inference and Learning in Modelling Financial Volatility * , 2004 .

[14]  Nikolaos V. Sahinidis,et al.  Optimization under uncertainty: state-of-the-art and opportunities , 2004, Comput. Chem. Eng..

[15]  Michael McAleer,et al.  A Survey of Recent Theoretical Results for Time Series Models with GARCH Errors , 2001 .

[16]  Werner Römisch,et al.  Airline network revenue management by multistage stochastic programming , 2008, Comput. Manag. Sci..

[17]  Philip Hans Franses,et al.  Nonlinear Time Series Models in Empirical Finance: Frontmatter , 2000 .

[18]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[19]  Michael McAleer,et al.  ASYMPTOTIC THEORY FOR A VECTOR ARMA-GARCH MODEL , 2003, Econometric Theory.

[20]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[21]  The Ten Commandments for Optimizing Value-at-Risk and Daily Capital Charges , 2009 .

[22]  Michael McAleer,et al.  Single Index and Portfolio Models for Forecasting Value-at-Risk Thresholds * , 2008 .

[23]  Michael McAleer,et al.  On Adaptive Estimation in Nonstationary Arma Models with Garch Errors , 2003 .

[24]  Huseyin Topaloglu.  A tighter variant of Jensen's lower bound for stochastic programs and separable approximations to recourse functions , 2009, Eur. J. Oper. Res..

[25]  Michael McAleer,et al.  An econometric analysis of asymmetric volatility : Theory and application to patents , 2007 .