Applicability Analysis of the AR-GARCH-t-X Model in Measuring Tail Risk in Carbon Finance Markets: VaR and ES Metrics

DOI: https://doi.org/10.62517/jel.202614229

Author(s)

Xinyue Du

Affiliation(s)

School of Business, Macau University of Science and Technology, Macau, China *Corresponding author

Abstract

Addressing the significant volatility clustering and leptokurtic heavy-tail characteristics of the carbon finance market, and the limitations of traditional normality models in measuring extreme risks, this paper constructs the AR-GARCH-t-X model, incorporating environmental externalities. This model aims to accurately quantify the impact of environmental shocks on the price fluctuations of EU (EUA) and CEA (CEA) carbon allowances through a dual transmission channel of policy regulation and investor sentiment. The study abandons the traditional normality assumption, employing a Student-t distribution to characterize residual characteristics, and systematically compares the measurement effectiveness of VaR (Value at Risk) and ES (Expected Loss). Empirical results show that the AR-GARCH-t-X model effectively captures structural risks caused by energy price fluctuations or sudden changes in the green index, with significantly higher prediction accuracy than the traditional GARCH model. Furthermore, the ES indicator, due to its consistent risk measurement properties and sensitivity to the intensity of tail losses, outperforms VaR in responding to extreme "black swan" events. The conclusions of this paper confirm the applicability of this model in carbon finance tail risk management, providing theoretical support and empirical evidence for regulatory agencies to construct differentiated early warning mechanisms and for investors to optimize carbon asset allocation.

Keywords

Carbon Financial Market; AR-GARCH-t-X Model; Environmental Externality; Tail Risk; Expected Loss (ES)

References

[1] Feng, Z. H., Wei, Y. M., Wang, K.: Estimating risk for the carbon market via extreme value theory: An empirical analysis of the EU ETS. Applied Energy 99, pp. 97-108(2012). [2] Bulai, V. C., Horobet, A., Popovici, O. C., Belascu, L., Dumitrescu, S. A.: A VaR-Based Methodology for Assessing Carbon Price Risk across European Union Economic Sectors. Energies 14, 8424(2021). [3] Liu, Y., Yang, A., Pei, H., Han, X.: Forecasting risk of European carbon emissions trading market with DySco-SKST model. Journal of Cleaner Production 434, 139933(2024). [4] Zhan, X., Li, Y.: Price Volatility and Risk Measurement of EU Carbon Futures under Structural Mutation. Academic Journal of Business & Management 7, pp. 15-22(2025). [5] Zhu, B., Sun, L. L.: Value-at-Risk Estimation of Carbon Spot Market Based on the Combined GARCH-EVT-VaR Model. Advanced Materials Research 1065-1069, pp. 3250-3253(2015). [6] Byun, S. J., Cho, H.: Forecasting carbon futures volatility using GARCH models with energy volatilities. Energy Economics 40, pp. 207-221(2013). [7] Yang, H., & Xu, H. Climate value at risk and expected shortfall for Bitcoin market[J]. Journal of Environmental Economics and Management, 2021, 111: 102415.Mi, Z. F., [8] Zhang, Y. J.: Estimating the 'Value at Risk' of EUA futures prices based on the Extreme Value Theory. International Journal of Global Energy Issues(2012).