The green transition of polluting firms is critical for achieving sustainable economic development. While previous research has explored the relationship between environmental policy and corporate pollution, it has often neglected the sustainability challenges faced by firms. Drawing on data from listed companies in China from 2008 to 2022, this paper empirically examines the impact of environmental policy on the risk-taking behavior of polluting firms. Building on this analysis, we assess the ecological impact, characteristics, and underlying mechanisms of a specific policy, while proposing solutions to promote sustainability in polluting firms. The findings indicate that, although environmental policy reduces the risk-taking levels of polluting firms, it has not been effective in curbing pollution emissions. This effect is particularly pronounced in firms exhibiting characteristics such as low-quality environmental information disclosure, industry resource crowding, and stringent regional assessments. The policy heightens financing constraints and investment costs for polluting firms and diminishes their expectations for future growth, ultimately suppressing both their capacity and willingness to take risks. Further analysis suggests that environmental coordination regulations and green transition guidance can encourage risk-taking behavior among polluting firms. These findings offer empirical evidence from the perspective of polluting firms, providing valuable insights into addressing the sustainability dilemma.

The Black–Scholes model laid the mathematical foundation for modern option pricing; however, its assumptions—stationary, independent, and Gaussian returns—are frequently violated in real markets, where long-memory volatility and sudden price jumps are well-documented. Two issues remain open: (1) Few option pricing models comprehensively incorporate long-memory and jump features. (2) The equivalence of the hedging, risk-neutral, and actuarial pricing methods, well-established under the standard Black–Scholes framework, has not been examined under jump–diffusion models. To address these gaps, we developed a sub-mixed fractional Brownian motion with Jumps (smfBm-J) model that jointly captures long memory, nonstationary increments, and jumps and derives a closed-form European call option pricing formula under the smfBm-J framework, highlighting the impact of model choice on valuation in incomplete markets.

The low-carbon transition has strengthened interactions between the cryptocurrency and carbon markets, while differences in cryptocurrency energy intensity may lead to heterogeneous risk spillover. We distinguish between energy-intensive and energy-efficient cryptocurrencies and use a multiscale quantile-on-quantile connectedness framework to examine spillovers in returns, volatility, skewness, and excess kurtosis. Three main findings emerge. First, connectedness is weak under normal market conditions but rises sharply when either market enters an extreme state. Return spillovers are concentrated mainly over short horizons, whereas volatility and higher-order risks show stronger connectedness over medium and long horizons. Second, net spillover roles vary across market states, investment horizons, and cryptocurrency types. Differences in energy intensity are particularly evident in volatility spillovers over long horizons and cross-state skewness transmission, while Ethereum shows a transitional pattern following its shift from proof-of-work to proof-of-stake. Third, the relative importance of direct and reverse connectedness varies across risk measures and horizons. These linkages are also sensitive to common external shocks, with major energy and monetary events producing distinct horizon-dependent responses. These findings highlight the importance of jointly considering energy intensity, higher-order risks, market states, and investment horizons in cross-market risk management.