A Break-Regime Score-Driven Model for Tail-Risk Forecasting in China’s Carbon Market Under Policy Shifts

Accurate tail-risk measurement in carbon markets is challenging because carbon allowance prices are shaped not only by heavy-tailed return dynamics, but also by policy changes that can alter the underlying risk dynamics. Models that ignore such structural shifts may perform reasonably well in normal periods while still understating downside risk when market conditions change. To address this issue, this paper proposes a break-regime generalized autoregressive score model with Student-t innovations, denoted as BR-GAS-t, for one-step-ahead forecasting of Value-at-Risk and Expected Shortfall. Using daily spot data from China’s carbon market, we compare BR-GAS-t with historical simulation, GARCH-N, GARCH-t, and regime-free GAS-t benchmarks. The results show that carbon returns are strongly heavy-tailed and that the post-break regime is characterized by stronger shock sensitivity, lower persistence, and a higher long-run conditional scale. Out-of-sample evidence further indicates that BR-GAS-t delivers the strongest overall VaR backtesting performance and the lowest average Fissler–Ziegel (FZ) loss in joint VaR–ES evaluation. Its advantage is most pronounced at the 2.5% and 1% tails, where downside risk is hardest to forecast. Robustness checks based on alternative break dates, window lengths, recursive schemes, and distributional assumptions confirm that the main conclusion is stable. The findings suggest that explicitly incorporating observed policy breaks improves tail-risk forecasting in policy-driven carbon markets.