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This paper analyses the volatility transmission between European Global Systemically Important Banks (GSIBs) and implied stock market volatility. A Dynamic Conditional Correlation Generalized Autoregressive Conditional Heteroskedasticity model is applied to determine the dynamic correlation between returns of Europe's GSIBs and the world's most prominent measure of market "fear", the CBOE Volatility Index (VIX). The results identify a higher negative co-relationship between the VIX and GSIB returns during the COVID-19 period compared with the Global Financial Crisis (GFC), with one-day lagged changes in the VIX negatively Granger-causing bank returns. The asymmetric impact of changes in implied volatility is examined by quantile regressions, with the findings showing that in the lower quartile–where extreme negative bank returns are present–jumps in the VIX are highly significant. This effect is more pronounced during COVID-19 than during the GFC. Additional robustness analysis shows that these findings are consistent during the periods of the Swine Flu and Zika virus epidemics. [ABSTRACT FROM AUTHOR]