Abstract: Carbon options are derivatives written on carbon futures that facilitate hedging, price discovery, and liquidity provision, thereby supporting carbon-market functioning and stability. However, carbon markets are highly sensitive to policy uncertainty, and returns display volatility clustering and heavy tails, posing challenges to accurate option valuation. Existing studies on carbon option pricing remain subject to notable limitations, motivating further theoretical and methodological development. Traditional option pricing approach assumes that return innovations follow the same distribution under the physical and risk-neutral measures, which limits its ability to capture non-normality features such as skewness and heavy tails. Moreover, in conventional approach, the dynamics of returns (and volatility) under the physical and risk-neutral measures are often constructed within a unified parameter system, implying that the volatility processes under the two measures share the same distribution because they are driven by identical parameters. This overly restrictive specification may lead to pricing errors. In addition, existing approaches often fail to fully exploit current return information for the timely updating of short-run volatility and rarely consider the effects of low-frequency policy uncertainty on the long-run volatility. Against this backdrop, in the paper we propose the Real-Time GARCH-MIDAS-FHS (RTGARCH-MIDAS-FHS) approach, which incorporates the Real-Time information (current return information) and the filtered historical simulation (FHS) approach, to value carbon options. In particular, this paper introduces the climate policy uncertainty (CPU) into the RTGARCH-MIDAS-FHS approach and proposes the RTGARCH-MIDAS-CPU-FHS approach to investigate the impact of CPU on carbon option prices. The RTGARCH-MIDAS-CPU-FHS approach allows the innovation distributions under the physical and risk-neutral measures to differ, thereby better accommodating the skewness and heavy-tailed features of carbon asset returns and potentially delivering more accurate option valuation. Moreover, from the perspective of information integration, we incorporate current return information into the short-run component to enhance the model’s responsiveness to abrupt volatility shocks, and introduce CPU into the long-run volatility via the MIDAS component, thereby structurally capturing the persistent effect of policy uncertainty on long-run volatility in the carbon market. Our empirical results based on the EUA options show that: (i) incorporating the current return information and the CPU index can improve the empirical return fitting of the underlying EUA futures; (ii) the aggravated change of the CPU index rises the long-run volatility of the EUA futures market; (iii) the RTGARCH-MIDAS-CPU-FHS approach outperforms the Black, the GARCH-FHS, the RTGARCH-FHS and the RTGARCH-MIDAS-FHS approaches in terms of both in-sample and out-of-sample pricing; (iv) the superior pricing performance of the RTGARCH-MIDAS-CPU-FHS approach is robust to alternative MIDAS lags, alternative versions of the CPU index, different market states, different sampling intervals, different pricing windows, and different option types.

Key words: climate policy uncertainty, current return information, carbon option pricing, GARCH-MIDAS, FHS approach