Modeling and the estimation of volatility in financial time series are important research subjects for which ARCH family models are recommended. These models are widely used to analyze volatility and manage risk in financial assets. In this study, share indices from the BRIC countries, Europe and the United States were analyzed to determine volatility in international indices. Current data was used to examine the period 1982-2021. Within this framework, the existence of asymmetric information, the leverage effect and the permanence of shocks were examined. Estimation results show the existence of asymmetric information. Bad news affects the system more than good news. The leverage effect is also experienced. Estimation results show that the shocks affecting the system are permanent. At the last stage, static foresight estimations were conducted on the explanatory power of the estimation results. Static foresight estimations present strong and weak evidence together. All parameters are statistically significant.