Value-at-risk estimates of the stock indices in developed and emerging markets including the spillover effects of currency market

This study derives the quantiles of the standardized generalized t (GT) in terms of a nonlinear equation which contains a regularized incomplete beta function. Then the quantiles are evaluated by utilizing Secant numerical approach to solve this nonlinear equation. Subsequently, the exponential generalized autoregressive conditional heteroskedasticity (EGARCH) model with GT distribution is utilized to estimate the corresponding volatility, and further estimate the value-at-risk (VaR) of seven stock indices in the developed and emerging markets. Empirical results show that, the stylized facts that appeared in most financial assets are seized effectively by this model and negative return and volatility spillover effects significantly subsist from the currency markets to stock markets. Moreover, the stock indices in emerging market have the higher return and the higher risk. As to VaR performance comparison, the modified historical simulation (MHS) and the EGARCH volatility specification significantly affect the VaR forecast performance for stock indices in the emerging market as compared with the developed market. Moreover, the VaR forecast performance of all models with GT is superior to that with normal return distribution only for stock indices in the developed market and only for 99% level. Turning to the whole market, the VaR forecast performance is almost the same as that for the emerging market. Finally, the MHS-EGARCH model with GT distribution is the optimal model to forecast the VaR among these eight models, irrespective of which of the three markets are used. This finding can provide the financial institutions to select an appropriate model to forecast and further control the market risk they faced.