We introduce a conditional volatility model that combines persistent volatility dynamics with spillovers from a wide cross-section of assets. We use elastic net estimation on a large, restricted VAR of realized measures to model these volatility dynamics. We show that despite the many parameters resulting from this wide cross-section, this spillover autoregressive (SPAR) realized variance model forecasts accurately and can be used in estimating large volatility spillover networks. These volatility spillover networks can be visualized and used to explain Granger-causal contagion in a group of assets. We apply this model to identify systemic risk across U.S. financial institutions over the period 2001-2010, and show that our model identifies systemic risk buildup over the 2007-2008 financial crisis.