Forecasting VaR, Using Conditional Density Models

Abstract The purpose of the work was to compare forecasting quality of VaR for two models: ARCD-ARCH and ARCD-ARCH with the addition of fundamental variables. The models were estimated for the daily logarithmic returns of the S&P500 for the period from 2000 to 2017. The sample was divided into 2 parts: the training (to estimate the coefficients) and the control (for comparison of models). The comparison was carried out using a logarithmic scoring model. The result showed the superiority of the forecast quality of the standard ARCD-ARCH model over the alternative. This phenomenon is probably a consequence of the explanation of the ARCH effect of trading volume, which leads to the elimination of the effect itself. This was tested using the construction of the EGARCH model with the inclusion of trading volume in the specification of the conditional variance. The coefficient for the fundamental variable turned out to be significant while the coefficients for the EGARCH variables turned out to be insignificant, which confirms the absence of the ARCH effect in the presence of trading volume as a regressor in the variance specification.