THE VALUE-AT-RISK OF THE STRAITS TIME INDEX : A COMPARISON OF ARCH MODELS

Abstract

This paper compares symmetric and asymmetric ARCH models for the estimation and forecasting of the volatility of the Strait Time Index (STI) as well as the computation of the value-at-risk (VaR) of the STI. The comparison is focused on the impact of leverage effect or asymmetric effect on the performance of the ARCH models and as a result, on the estimation of the VaR. Using 6 years of daily and weekly data from January 1993 to October 1998, ARCH (4), GARCH (1,1), EGARCH (1,1) and TARCH (1,1) models are used to estimate and forecast the volatility of the STI. The forecasted standard deviations from these models are used to compute the VaR of the STI. Goodness-of-fit diagnostics tests indicate that the TARCH model fits the daily and weekly STI better as compared to the other models. In the regression test for in­ sample forecasting ability, the TARCH model appears to contain more information than the others, especially for daily data. Kupiec' s frequency of excessive loss test, which is used to verify the estimation of VaR, shows that the TARCH model's performance is the best. The empirical results suggest that the TARCH model is the best performing model. This indicates the importance of leverage effect in the STI. Failure to take into account the leverage effect affects the performance of the ARCH models and results in biased VaR estimates. In addition, different methods of estimating the conditional variance and capturing the leverage effect under the various ARCH models also matter. Thus, the choice of the appropriate ARCH model is important.