Decay factor optimisation in time weighted simulation -- Evaluating VaR performance
We propose an optimisation approach for determining the optimal decay factor in time weighted (BRW) simulation. The backtesting of the BRW simulation, which involves different decay factors, together with a broad range of competing VaR models, has been performed on a sample of seven stock indexes and two commodities: gold and WTI oil. The results obtained show that the BRW simulation with an optimised decay factor relative to the Lopez (1998) size-adjusted function is among the best performing VaR models, second only to the conditional extreme value approach (McNeil & Frey, 2000). The optimised decay factors are sufficiently stable over time, giving economic justification to the optimisation because they do not change over longer time periods. Unlike most of the VaR models tested, in the large majority of cases, the optimised BRW model passes the Basel II criteria but yields significantly lower VaR forecasts than the extreme value approaches, thus resulting in a lower idle capital, i.e. lower costs.
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- Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
- McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
- Jose A. Lopez, 1999.
"Methods for evaluating value-at-risk estimates,"
Federal Reserve Bank of San Francisco, pages 3-17.
- Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
- Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Economic Policy Review, Federal Reserve Bank of New York, issue Apr, pages 39-69.
- Matthew Pritsker, 2001. "The hidden dangers of historical simulation," Finance and Economics Discussion Series 2001-27, Board of Governors of the Federal Reserve System (U.S.).
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