The growing interest and direct impact of carbon trading in the economy have drawn an increasing attention to the evolution of the price of CO2 allowances (European Union Allowances, EUAs) under the European Union Emissions Trading Scheme (EU ETS). As a novel financial market, the dynamic analysis of its volatility is essential for policymakers to assess market efficiency and for investors to carry out an adequate risk management on carbon emission rights. In this research, the main autoregressive conditional heteroskedasticity (ARCH) models were applied to evaluate and analyze the volatility of daily data of the European carbon future prices, focusing on the last finished phase of market operations (phase III, 2013–2020), which is structurally and significantly different from previous phases. Some empirical findings derive from the results obtained. First, the EGARCH (1,1) model exhibits a superior ability to describe the price volatility even using fewer parameters, partly because it allows to collect the sign of the changes produced over time. In this model, the Akaike information criterion (AIC) is lower than ARCH (4) and GARCH (1,1) models, and all its coefficients are significative (p< 0.02). Second, a sustained increase in prices is detected at the end of phase III, which makes it possible to foresee a stabilization path with higher prices for the first years of phase IV. These changes will motivate both companies and individual energy investors to be proactive in making decisions about the risk management on carbon allowances.