With the rapid growth of the carbon market, carbon price fluctuations are increasingly important for market participants. Carbon market risk directly affects the investor confidence and emission reduction results. In the present study, extreme value theory (EVT) is used to analyze risk exposure for carbon price and to measure the Value at Risk (VaR) for the carbon market. GARCH models are applied to establish a model of price volatility for the spot market and the futures market and to calculate dynamic VaR. Traditional VaR and VaR based on EVT are also compared. The results show that the downside risk is higher than the upside risk for the carbon market. Upside and downside risks are higher in the first phase (June 2005-December 2007) than in the second phase (February 2008-December 2009) for both the spot and futures markets. Upside and downside risks are similar for the spot and futures markets during the same phase. The results also show that the EVT VaR is more effective than the traditional method, which can reduce the risks for market participants. Dynamic VaR based on GARCH and EVT can effectively measure the EU ETS market risk. (C) 2012 Published by Elsevier Ltd.