• value-at-risk;
  • historical simulation;
  • volatility;
  • Garman-Klass estimator


We propose a method approach. We use six international stock price indices and three hypothetical portfolios formed by these indices. The sample was observed daily from 1 January 1996 to 31 December 2006. Confirmed by the failure rates and backtesting developed by Kupiec (Technique for verifying the accuracy of risk measurement models. Journal of Derivatives 1995; 3: 73–84) and Christoffersen (Evaluating interval forecasts. International Economic Review 1998; 39: 841–862), the empirical results show that our method can considerably improve the estimation accuracy of value-at-risk. Thus the study establishes an effective alternative model for risk prediction and hence also provides a reliable tool for the management of portfolios. Copyright © 2011 John Wiley & Sons, Ltd.