Recent research shows that the efforts to limit climate change should focus on reducing the emissions of carbon dioxide over other greenhouse gases or air pollutants. Many countries are paying substantial attention to carbon emissions to improve air quality and public health. The largest source of carbon emissions from human activities in some countries in Europe and elsewhere is from burning fossil fuels for electricity, heat, and transportation. The prices of fuel and carbon emissions can influence each other. Owing to the importance of carbon emissions and their connection to fossil fuels, and the possibility of [1] Granger (1980) causality in spot and futures prices, returns, and volatility of carbon emissions, crude oil and coal have recently become very important research topics. For the USA, daily spot and futures prices are available for crude oil and coal, but there are no daily futures prices for carbon emissions. For the European Union (EU), there are no daily spot prices for coal or carbon emissions, but there are daily futures prices for crude oil, coal and carbon emissions. For this reason, daily prices will be used to analyse Granger causality and volatility spillovers in spot and futures prices of carbon emissions, crude oil, and coal. As the estimators are based on quasi-maximum likelihood estimators (QMLE) under the incorrect assumption of a normal distribution, we modify the likelihood ratio (LR) test to a quasi-likelihood ratio test (QLR) to test the multivariate conditional volatility Diagonal BEKK model, which estimates and tests volatility spillovers, and has valid regularity conditions and asymptotic properties, against the alternative Full BEKK model, which also estimates volatility spillovers, but has valid regularity conditions and asymptotic properties only under the null hypothesis of zero off-diagonal elements. Dynamic hedging strategies by using optimal hedge ratios are suggested to analyse market fluctuations in the spot and futures returns and volatility of carbon emissions, crude oil, and coal prices.