Value-at-risk estimation via a semi-parametric approach: Evidence from the stock markets

Abstract

This study utilizes the parametric approach (GARCH-based models) and the semi-parametric approach of Hull and White (Journal of Risk 1: 5–19, 1998)(HW-based models) to estimate the Value-at-Risk (VaR) through the accuracy evaluation of accuracy for the eight stock indices in Europe and Asia stock markets. The measure of accuracy includes the unconditional coverage test by Kupiec (Journal of Derivatives 3: 73–84, 1995) as well as twoloss functions, quadratic loss function, and unexpected loss. As to the parametric approach, the parameters of generalized autoregressive conditional heteroskedasticity (GARCH) model are estimated by the method of maximum likelihood and the quantiles of asymmetric distribution like skewed generalized student′s t (SGT) can be solved by composite trapezoid rule. Sequentially, the VaR is evaluated by the framework proposed by Jorion (Value at Risk: the new benchmark for managing financial risk. New York: McGraw-Hill, 2000). Turning to the semi-parametric approach of Hull and White (Journal of Risk 1: 5–19, 1998), before performing the traditional historical simulation, the raw return series is scaled by a volatility ratio where the volatility is estimated by the same procedure of parametric approach. Empirical results show that the kind of VaR approaches is more influential than that of return distribution settings on VaR estimate. Moreover, under the same return distributional setting, the HW-based models have the better VaR forecasting performance as compared with the GARCH-based models. Furthermore, irrespective of whether the GARCHbased model or HW-based model is employed, the SGT has the best VaR forecasting performance followed by student′s t, while the normal owns the worst VaR forecasting performance. In addition, all models tend to underestimate the real market risk in most cases, but the non-normal distributions (student′s t and SGT) and the semi-parametric approach try to reverse the trend of underestimating.​