Equilibrium bifurcation and extreme risk in the EU carbon futures market.

Considering the long-term memory and volatility clustering of the European Union (EU) Carbon Emission Allowances (EUA) futures returns, based on the economy-energy-environment system perspective and the assumption of investors' heterogeneity, this study proposes a joint modeling approach combining the fractionally integrated generalized autoregressive conditional heteroscedasticity model (FIGARCH) and the stochastic cusp catastrophe model (SCC) to examine the equilibrium bifurcations and extreme risks in the EU carbon futures market. The relevant results are threefold. (1) The SCC model has good fitting effect and interpretability, and is an effective method for investigating catastrophe reactions under time-varying volatility conditions. (2) In the EUA futures market, chartists are mainly affected by short-term price and trading volume changes, which leads to the emergence of equilibrium bifurcations, while fundamentalists make investment decisions based on the economy, the energy market, and market supply-demand, which affects the asymmetry of equilibrium bifurcations. (3) Using the catastrophe criterion (i.e., Cardan's discriminant of the equilibrium surface equation), we identify148 equilibrium bifurcation time points in the EUA futures market from December 3, 2009 to September 16, 2020, most of which are concentrated in two upward periods with an average scale of extreme risks is about 32.51 %. Our analysis provides theoretical support for regulatory authorities to stabilize the carbon futures market and build a collaborative extreme risk management framework covering energy and macroeconomics, also proposing suggestions for traders to effectively prevent extreme risks.