The European Union Emission Trading Scheme (EU ETS) has established a pricing system for carbon emissions. As the new commodity may increase the diversification of a financial portfolio and reduce the overall investment risk, a deeper investigation of its properties is needed. Investigating the link between carbon and other asset classes, such oil and stock markets, is important to understand how carbon market interacts with other financial markets. Empirical results indicate that carbon futures returns do respond positively to oil returns shock. A shock in oil price initially has a positive impact on stock market. The multivariate generalized autoregressive conditional heteroskedasticity (GARCH) of the BEKK model indicate that oil market has an effect on the volatility of the other two markets but it is much less affect by them. These results should be useful for policy makers, portfolio managers and others interested in this rapidly developing field of finance.