In this paper, we propose the copula-mixed frequency data sampling model incorporating time-varying risk aversion (RA) (copula-MIDAS-RA model) to investigate the impact of time-varying RA on the dynamic dependence between crude oil futures and European Union allowance (EUA) futures markets. An empirical analysis based on the daily data on the Brent crude oil futures and EUA futures returns and the monthly data on the RA index shows that the Student-t copula-MIDAS-RA model has better goodness-of-fit than other copulas, suggesting that the tail dependence between crude oil futures and EUA futures markets is symmetric and time-varying. More importantly, we observe that the RA has a significantly positive impact on the dynamic dependence between crude oil futures and EUA futures markets. That is, the dynamic dependence between crude oil futures and EUA futures markets is expected to increase with the level of RA increases. Moreover, we observe that the Student-t copula-MIDAS-RA model improves the accuracy in risk management relative to other copula models. Our findings have implication for hedging strategies and asset pricing.