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This article applies two measures to assess spillovers across markets: the Diebold and Yilmaz's (2012) spillover index and the Hafner and Herwartz's (2006) analysis of multivariate GARCH models using volatility impulse response analysis. We use two sets of data, daily realized volatility (RV) estimates taken from the Oxford-Man RV library, for the S&P500 and the FTSE, plus 10 years of daily returns series for the New York Stock Exchange Index and the FTSE 100 index. Both data sets capture both the global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The spillover index captures the transmission of volatility to and from markets, plus net spillovers. The Volatility Impulse Responses (VIRF) have to be calibrated to conditional volatility estimated at a particular point in time. We explore the impact of three different shocks, the onset of the GFC, the height of the GFC, and the impact of the ESDC. Our modelling includes leverage and asymmetric effects applying a multivariate GARCH model, and further analysis using both BEKK and diagonal BEKK (DBEKK) models. We find the impact of negative shocks is larger, but shorter in duration, in this case a difference between 3 and 6 months. [ABSTRACT FROM AUTHOR]