Comparison of semi-parametric and benchmark value-at-risk models in several time periods with different volatility levels

In the literature, there is no consensus as to which Value-at-Risk forecasting model is the best for measuring market risk in banks. In the study an analysis of Value-at-Risk forecasting model quality over varying economic stability periods for main indices from stock exchanges was conducted. The VaR forecasts from GARCH(1,1), GARCH-t(1,1), GARCH-st(1,1), QML-GARCH(1,1), CAViaR and historical simulation models in periods with contrasting volatility trends (increasing, constantly high and decreasing) for countries economically developed (the USA – S&P 500, Germany - DAX and Japan – Nikkei 225) and economically developing (China – SSE COMP, Poland – WIG20 and Turkey – XU100) were compared. The data samples used in the analysis were selected from the period 01.01.1999 – 24.03.2017. To assess the VaR forecast quality: excess ratio, Basel traffic light test, coverage tests (Kupiec test, Christoffersen test), Dynamic Quantile test, cost functions and Diebold-Marino test were used. Obtained results show that the quality of Value-at-Risk forecasts for the models varies depending on a volatility trend. However, GARCH-st (1,1) and QML-GARCH(1,1) were found to be the most robust models in the different volatility periods. The results show as well that the CAViaR model forecasts were less appropriate in the increasing volatility period. Moreover, no significant differences for the VaR forecast quality were found for the developed and developing countries.