The Effects of Estimation Methods of Stock Price Volatility on VaR Open Access

I perform the backtesting of 10-day VaR's using daily returns of KOSPI 200 from January 1994 to December 1993 (2,692 days). The seven volatility measures are calculated with the last 300-day data; those are the historical standard deviations, the exponentially weighted moving average (EWMA) volatilities, the standard deviations from GARCH (1, 1) and three measures to consider autocorrelations in daily returns. The seven types of ten-day VaR’s at 1 % and 5% significance levels are estimated from these six volatility measures and 1 or 5 percentile of the last 300-day historical distributions I use the likelihood ratio (LR) test statistics to test the expected frequency and/or independence of the occurrence of extreme losses, that is, the losses which exceed the VaR values. The LR statistics for the expected frequence show that the VaR measure based on the historical standard deviations is the best one, but the LR statistics for independence reject the usefulness of ali the VaR measures.