This paper computes a new financial globalization index for a large sample of countries for 1992-2016. Unlike other measures, the financial globalization index corrects for the heteroscedasticity of global volatility. This leads to a downward adjustment of financial globalization trends for developed, emerging, and frontier markets. The paper also shows that financial globalization reduces market volatility (measured by the volatility of stock returns) in tranquil times, and increases it in turbulent ones. On average, the first effect dominates, so that financial globalization leads to a decrease in market volatility, which is more pronounced in frontier markets.