Policy-State Gated Regime Dynamics in European Emission Allowance Futures

Technical Summary: Policy-State Gated Regime Dynamics in European Emission Allowance Futures

Problem and Motivation
European Union Allowance (EUA) futures are unique financial assets created by regulatory policy rather than natural scarcity. Their return dynamics are driven by a complex interplay of regulatory supply schedules (specifically the Market Stability Reserve or MSR), compliance demand, fuel-switching incentives, and financial trading activity. While existing literature has established that EUA returns exhibit non-Gaussian features, volatility clustering, and regime dependence, standard latent Markov-switching models often fail to link these unobserved states to the specific observable policy and market variables that define the EU ETS.

The core problem addressed is whether the transition probabilities between low-stress and high-stress return regimes can be explicitly modeled as a function of observable policy-state variables (surplus), energy-market stress, and trading activity, rather than being inferred solely from past returns. The authors argue that a "policy-state gated" approach is necessary to understand the law of motion of EUA returns under changing market designs, particularly following the 2023 EU ETS reforms.

Methodology
The paper estimates a two-state, time-varying transition probability (TVTP) Markov model for daily EUA futures returns. The model is specified as follows:

1. State Dynamics: The return $r_{t+1}$ follows a normal mixture distribution conditional on a latent state $Z_t \in \{0, 1\}$, where state 0 represents a low-stress regime and state 1 represents a high-stress regime. The states are distinguished primarily by conditional volatility ($\sigma_0 < \sigma_1$).
2. Policy-State Gating: Unlike standard latent Markov models where transition probabilities are constant, the transition law here depends on a vector of observable gate variables $G_t = (\tilde{s}_t, \tilde{\tau}_t, \tilde{g}_t, \tilde{v}_t)'$:
   • $\tilde{s}_t$: A standardized market-implied price-state proxy (rolling percentile of EUA prices).
   • $\tilde{\tau}_t$: Standardized Total Number of Allowances in Circulation (TNAC), the official surplus measure used for MSR operations.
   • $\tilde{g}_t$: Standardized 21-day annualized volatility of Dutch TTF gas prices (energy-market stress).
   • $\tilde{v}_t$: Standardized log volume of EUA futures (market activity).
3. Transition Equation: The probability of remaining in or transitioning to a state is modeled via a logistic function:
   $$p_{i0,t} = \Lambda(a_{i0} + b_{i0}^{(s)}\tilde{s}_t + b_{i0}^{(\tau)}\tilde{\tau}_t + b_{i0}^{(g)}\tilde{g}_t + b_{i0}^{(v)}\tilde{v}_t)$$
   where $\Lambda$ is the logistic function. This structure allows the transition probabilities to shift dynamically based on observable market conditions.
4. Estimation and Evaluation: The model is estimated via Maximum Likelihood using the Hamilton filter on a common sample from May 15, 2019, to May 28, 2026. The authors employ a nested model comparison strategy, progressing from a Gaussian IID benchmark to a latent Markov model, and finally to the full policy-gated specification.
5. Benchmarks: The proposed model is rigorously compared against:
   • Latent Markov models with constant transition probabilities.
   • Nested Markov models with subsets of gate variables.
   • Heavy-tailed GARCH-family benchmarks (Student-t GARCH, GJR-GARCH, EGARCH) to test density forecasting performance.
6. Validation: Evaluation includes common-sample likelihood (AIC/BIC), one-step-ahead stress ranking (AUC, hit rates), and held-out validation using fixed train-validation-test splits to assess real-time forecasting dominance.

Key Results

• Regime Dependence: The data strongly rejects a single-regime Gaussian model. A latent two-regime Markov model significantly improves the fit (lower AIC) over the IID benchmark, confirming that EUA returns are state-dependent and heavy-tailed.
• Value of Observable Gates: Within the Gaussian Markov family, the full policy-gated model provides the best fit (lowest AIC) compared to latent or partially gated models. The inclusion of TNAC, gas volatility, and trading activity adds incremental information to the transition law. However, the full gate does not outperform the latent model by BIC, and heavy-tailed GARCH models (Student-t variants) remain superior in terms of both AIC and BIC for unconditional density fitting.
• Economic Interpretation of Coefficients:
  • TNAC: Higher TNAC (surplus) is associated with a higher probability of transitioning from low-stress to high-stress states, though the effect is estimated with wide uncertainty intervals due to the low frequency of TNAC updates.
  • Gas Volatility: Higher TTF gas volatility is the strongest driver, significantly increasing the probability of entering and remaining in the high-stress regime.
  • Trading Activity: High volume appears to act primarily as a persistence mechanism for the high-stress state rather than a simple entry trigger.
  • Price State: The market-implied price proxy shows asymmetric effects, increasing stress entry probability at high levels but facilitating exit from stress.
• Forecasting Performance: In common-sample exercises, the policy-gated model modestly outperforms GARCH benchmarks in ranking absolute-tail stress days (AUC ~0.70 vs. ~0.67). However, in held-out validation (crisis and post-crisis periods), the GARCH models consistently outperform the Markov model in log scores, Brier scores, and VaR calibration. The Markov model does not establish real-time forecasting dominance.

Significance and Claims
The paper explicitly frames its contribution as interpretive and associative rather than causal or universally predictive.

• Interpretive Value: The primary contribution is demonstrating that observable policy surplus (TNAC), energy volatility, and market activity are statistically associated with the timing and persistence of EUA return regimes. This provides a transparent map from EU ETS institutional variables to the probability of market stress, which latent models cannot offer.
• Bounded Forecasting Claims: The authors modestly claim that while the policy-gated model improves regime classification and economic interpretation, it does not replace heavy-tailed volatility models for density forecasting or real-time risk management. The model is presented as a tool for understanding the law of motion of regimes under specific policy and market conditions, rather than a superior standalone forecasting engine.
• Policy Relevance: The results suggest that the "endgame" of the EU ETS, characterized by tightening caps and MSR interventions, creates a market environment where regime transitions are driven by observable policy and energy shocks, necessitating models that explicitly incorporate these state variables.

In summary, the paper successfully constructs a regime-switching model where transition probabilities are gated by observable EU ETS variables, offering a deeper economic understanding of carbon market dynamics, while acknowledging that traditional volatility models remain more robust for pure density forecasting.