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A decision rule to minimize daily capital charges in forecasting value‐at‐risk
Author(s) -
McAleer Michael,
JimenezMartin JuanAngel,
PérezAmaral Teodosio
Publication year - 2010
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.1167
Subject(s) - capital requirement , basel ii , capital (architecture) , economics , risk adjusted return on capital , profit (economics) , index (typography) , value at risk , capital adequacy ratio , value (mathematics) , econometrics , economic capital , actuarial science , risk management , computer science , microeconomics , financial capital , finance , capital formation , archaeology , machine learning , world wide web , history
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.