Journal of Risk

Incorporating volatility updating into the historical simulation method for value-at-risk

John Hull and Alan White


This paper proposes a procedure for using a GARCH or exponentially weighted moving average model in conjunction with historical simulation when computing value-at-risk. It involves adjusting historical data on each market variable to reflect the difference between the historical volatility of the market variable and its current volatility. The authors compare the approach using 9 years of daily data on 12 exchange rates and 5 stock indices with more commonly used historical simulation approaches and show that it is a substantial improvement.

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