The futures trading scheme has existed in the financial industry for a long time. Currently, actively traded products include commodity futures and financial futures. Basically, the futures market is a place for risk transfer, it offers hedging and price discovery function. Specifically, manufacturing enterprises play the role of hedgers, while financial institutions and private investors act as speculators (sometimes are hedgers too), the former is commonly risk-averse, but the latter is risk-tolerant. Thus, the hedger can transfer the price risk to the speculators, as a price they give up the chance to obtain excess income. What’s more, due to the abundant information brought by the participants, the futures prices are very close to the actual value, which helps to realize the price discovery function.

The carbon futures trading scheme is similar to the general financial futures trading scheme. The ETS-covered power enterprises play the role of hedgers, they are extremely risk-averse. Therefore, it is assumed that the main purpose for them to participate in the carbon futures market is to hedge the risk of carbon price volatility, the net effect of hedging is locking in the executive carbon price, though the actual price level varies over time. In short, the determined ECP can be taken as the proxy for carbon futures trading.

The permanent goal for enterprises is to seek for the maximum profits. Here, the OPDP is employed to determine the optimal mitigation amount for the ETS-covered power enterprises in the context of carbon futures trading. Some basic assumptions are adopted in this model, which help the model be more realistic. Firstly, the allowance allocation rule is assumed to be the benchmark method. Currently, free allocation distribution in China’s pilot carbon market is realized through a mixed method of “grandfathering and benchmarking,” however, the latter is expected to be the dominant allocation method in the forthcoming China’s national carbon market (Zhang et al., 2015; Yang et al., 2020). Secondly, the distribution of consumers’ low-carbon awareness is assumed to be the β distribution (Gao, 2006) rather than the commonly used uniform distribution (Ye et al., 2017; Yang and Liu, 2016; Han, 2018), for the latter ignores the heterogeneity of consumers’ low-carbon awareness. Thirdly, the subsidy level is comparable to those mentioned in the policy of Ultra-low Emission Retrofit Plan ³ . As a result, the subsidy factor used in the model is derived based on this policy. Finally, the consumers’ low-carbon awareness can be realized through free choice of the electricity source. As we all know, electricity consumed in China is generally supplied by the State Grid Corporation of China and China Southern power grid, so the source of consumed electricity is hard to determine, which means that consumers’ desire to use green electricity is hard to realize. Nonetheless, thanks to the on-going reform of the electricity market, consumers can potentially have the right to choose the electricity sources (thermal-power, PV, wind, etc.).

The general ideas of this model is that power producers will change their production plan according to the market feedbacks, which includes the carbon emission costs, subsidies for greener production and green electricity prices, etc. Through this model, we can derive what should be the most profitable optimal emission reductions in the context of carbon futures trading. The following part will present the model in detail.

Eq. 1 shows the number of free allowances that the ETS-covered power enterprises can obtain under the benchmarking allocation rule. Eq. 2 displays the distribution of consumers’ low-carbon awareness δ, which as stated previously, follow the β distribution. Suppose the general low-carbon awareness of the consumers is relatively low, we can take α = 1 ,   β = 3 . Then we can derive Eq. 3 as the possible low-carbon consumption of a consumer who has the low-carbon awareness δ . e m = a * Q * b sec (1) f ( x ) = 1 B ( α , β ) x ( α − 1 ) ( 1 − x ) ( β − 1 ) (2) F ( X ) = ∫ δ 1 f ( x ) d ( x ) = ( 1 − δ ) 3 (3)

As for the number of emission reductions by the enterprises, two ideas are considered in our model: the actual mitigation amount e r d is defined as the mitigation amount compared to the previous period e h , as expressed by Eq. 4; and the tradeable emission reduction amount e o d is the gap between free allowance amount e m and the actual emission amount e c , which is expressed by Eq. 5. Government subsidy is a great push to the low-carbon transition in the power sector. It is assumed that the subsidy level is comparable to that in the Ultra-low Emission Retrofit Plan, which is mainly comprised of the electricity price subsidy (generally 0.01 CNY₂₀₁₈/kW·h) and power generation hour bonus (commonly 200 h). Consequently, we set the overall subsidy for emission reduction as ϕ = 600 CNY₂₀₁₈/tonnes CO₂e. Eq. 6 shows the price spilling over effect of electricity produced by ETS-covered power enterprises; basically, the price gap between the green electricity and common electricity is filled by consumers’ low-carbon awareness and government subsidy. As for the demand for green electricity, it can be calculated as the product of low-carbon consumption possibility and sectoral demand, as expressed by Eq. 7. e r d = e h − e c (4) e o d = e m − e c (5) P − P 0 = K ( δ − δ 0 ) + ϕ e r d (6) q = q sec F ( x ) (7)

Finally, we can derive the general profit of the enterprises in Eq. 8. Pertaining to the mitigation cost, following by a literature review (Gao et al., 2004; Zhang et al., 2015; Zhou et al., 2016; Han, 2018) we conclude that it should take a unary quadratic function form, which is shown in Eq. 9. Table 1 sets out the meanings and specific values of parameters in the model. π = ( P − C ) q − C d ( e r d ) + ϵ e o d (8) C d ( e r d ) = γ e r d 2 + η e r d (9)

To derive the optimal mitigation amount, we firstly let the derivative of profit π ′ ( P ) equals 0 as a means of getting the green electricity price P, we then let the marginal emission reduction cost equals the margin emission reduction benefits to derive the optimal mitigation volume emission reduction, as expressed in Eqs 10, 11 separately. π ′ ( P ) = ( ( P − C ) q − C d ( e r d ) + ϵ e o d ) ′ ( P ) = 0 (10) C d ′ ( e r d ) = ε + ( ( P − C ) q ) ′ ( e r d ) = 0 (11)

Life Cycle Assessment (LCA) is widely used to determine the life cycle impact of a product (Di et al., 2007; Gerbinet et al., 2014). Our paper focuses on the life cycle impact assessment of electricity. As we all know, electricity can be produced through many approaches; however, the most relevant approaches in our study are coal-fired power units, PV and wind. Different technical trajectories exist even in the same kind of approach, but for the convenience of analysis, we choose Sub-C, Super-C and USC units for the coal-fired power units; mono-crystal silicon photovoltaic (mono-Si PV) for PV; and DFIGs for wind (see reasons for selection in Section 3.1).

Emission inventory data was collected from existing researches. Literatures quoted have a common feature that the function unit is the production of 1 kW·h electricity. The actual process of different technologies differs. In detail, the LCA for the coal-fired units includes coal-mining, coal transportation and electricity generation process (Liang et al., 2013); the mono-Si PV includes raw material extraction, manufacture of cell and module fabrication, assembling, transportation, application and decommissioning (Celik et al., 2016); DFIG of wind includes raw material supply, manufacturing phase, transportation and assembly process, operation and maintenance phase, dismantling, recycling and waste disposal (Siddiqui and Dincer, 2017).

Regarding the LCIA method, ReCiPe 2016 (Huijbregts et al., 2017) is widely applied (Bergesen et al., 2014; Celik et al., 2016; Huang et al., 2017; Rauner et al., 2020). After comparing ReCiPe2016 and other LCIA methods, it is found that this approach performs better in the context of China for some impact factors are specifically prepared for China; thus, the ReCiPe2016 is selected as the LCIA method in this study. As for the impact categories, we chose Global Warming Potential, Particular Matter, Acidification, Eutrophication and other impact categories from the overall 17 midpoint level impact categories, and the Damage to Human Health and Damage to Ecosystems from the three endpoint level impact categories. The endpoint-level impact categories are used for further calculation, which is to monetize the environmental impacts of 1 kW·h electricity production by different technologies.

The environmental impacts of a product can be understood well through performing LCIA analysis; however, these impact categories are hard to compare since their metrics vary a lot. Monetization is a good pathway to solve this problem, much monetization work has been carried out, from the human health impact (Partridge and Gamkhar, 2012; Gao et al., 2015; Cai et al., 2018; Wang et al., 2020) to ecosystem damage (Rauner et al., 2020).

(Rauner et al., 2020) gave a good example in the monetization of environmental damage field, we quoted their monetarization factors and made some adjustments to transform the data to make it better fit in the context of China. In detail, the damage to human health is measured by the unit of Disability Adjusted Life Years (DALY), as 1.936 Million CNY₂₀₁₈/DALY; the damage to ecosystem is quantified through species per year loss, the value is set as 1.823 Billion CNY₂₀₁₈/(species·year).

Another important aspect is the cost of rising temperatures, which is primarily caused by Greenhouse Gases (GHGs). First of all, we need to determine the actual temperature rise caused by GHG emissions. Matthews gave a reference that the ambient temperature tends to rise 1.8°C for every 1,000 Gt CO₂e emissions (Matthews et al., 2012). Therefore, with the carbon emission inventory and consumed quantity of electricity, the exact temperature rise T A T ( t ) can be determined. Next, we need to transform the temperature rise into actual economic loss. Nordhaus (2017), who developed the DICE (Dynamic Integrated Climate-Economy) and RICE (Regional Integrated Climate-Economy) models, leads in this field. In the DICE 2013R version, Nordhaus used the monetized estimates of economic losses which are conducted by Tol (2010) as the basis of the damage function. The damage function is defined as: Ω ( T ) = D ( T ) 1 + D ( T ) (12) D ( T ) = φ 1 * T A T ( t ) + φ 2 * T A T ( t ) 2 (13) φ 1 , φ 2 : coefficient T A T ( t ) : the exact temperature rise caused by GHGs emissions

According to the final estimates carried out by Nordhaus (2017), a 3°C warming will cause a global income loss of 2.1%, and a 6°C warming will cause a loss of 8.5%. The coefficient is calculated to be φ 1 = −0.135% and φ 2 = 0.28%, which is consistent with results derived by (Lamperti et al., 2019).

Founded by Holland (1997) in the 1970s, the Genetic Algorithm (GA) has been widely used in the optimization field (Fatemi Aghda and Mirfakhraei, 2020; Yeh et al., 2020). Through imitating the natural selection and biological evolution process, the GA can find the best solution for the optimization problem. The basic idea for GA is, in the biological evolution process, those who survived were best adapted to the changing environment. In its mathematical counterpart, the principle is that only those who can best satisfy the constraints should be selected as the overall optimal solution, while those failed to satisfy the constraints will be weeded out.

In our study, the objective is to find the decarbonization roadmap which has the maximum environmental benefits, which is expressed in Eq. 14. According to the specific condition of our goal, nine constraints are included, which are displayed in Table 2. Furthermore, the number of evolving generations is set to be 3,000.

Objective function: total environmental benefits should be maximized max ⁡   { ∑ i = 1 5 ( E Q s c , i * ( ∆ D T H i + ∆ D T E i + ∆ G D P L i ) (14) E Q s c , i : electricity volume that should be produced by trajectory i (TR i) ∆ E R i : difference of emission reduction for trajectory i (TR i)

The ultimate target of carbon futures trading is to vector better emission reduction trajectories. Normally, such trajectories include the optimization of production processes, upgrading production techniques, limiting the operating hours of low-efficiency coal-fired power units or just simply buying allowances to satisfy the emission cap. Chinese coal-fired power plants have gone through the Ultra-low Emission Retrofit Plan since 2015. The latest review reported that over 86% of the coal-fired units now satisfy the emission limits (China Electricity Council, 2020), which indicates that the potential of optimizing the production processes is quite limited. Thus, the choices for ETS-covered power enterprises remain upgrading production techniques, renewable energy investments, carbon allowance trading and adjusting operational strategies (e.g., cutting down the utilization hours of low efficiency thermal units). In this paper, the pathways of production techniques upgrading and renewable energy investment are mainly considered, with the aim of achieving around 36% of the total emission reduction.

Five trajectories are considered when planning the optimal decarbonization roadmap: (TR1) Sub-C replaced by Super-C; (TR2) Super-C replaced by USC; (TR3) Sub-C replaced by USC; (TR4) newly installed mono-Si capacity; (TR5) newly installed DFIG capacity. It is worth noting the basis for this design: the Sub-C coal-fired units generally emit more than Super-C, and much more than USC and renewable energies. Therefore, the Sub-C units should be phased out firstly. As shown in Figure 2B, the newly installed thermal power capacity is mainly composed of the Super-C and USC units. The Super-C units are much more environmentally friendly than Sub-C, but perform worse than USC, further, as commercialized USC units are becoming available according to Figure 2A, in trajectory 2 we consider the possibility of replacing Super-C with USC units.

Emission reductions are difficult to achieve with regard to coal-fired power plants, and consequently power enterprises are becoming more and more interested in renewable energy rather than fossil fuel. As shown in Figure 3, the installed thermal power capacity is decreasing while the PV and Wind are increasing, and the volume of non-thermal power new investment is larger than 70% in recent years (see the spline in Figure 3). In practice, China Huaneng Group, one of the largest power enterprises in China, installed mainly PV and Wind capacity in year 2019 (Juchao Information Network, 2019b), which is echoed by GD Power Development Co., Ltd. (Juchao Information Network, 2019a). PV and Wind seem to be currently the most promising renewable energies ⁴ and some researchers suggested that clean energy investment would help enterprises better adapt to China’s national carbon market (Yu et al., 2020). Consequently, in trajectories 4 and 5, we choose to newly install PV and Wind capacity. However, PV includes three generations of cells which have different environmental impacts, and the Wind industry also includes many types. After investigation, we finally choose mono-Si for PV and DFIG for Wind since their performance and market share are much better or larger [(Celik et al., 2016) and Bloomberg ⁵ ].

To calculate the total optimal emission reduction for the next 10 years, a reasonable prediction on thermal electricity production and newly installed capacity are necessary, which are influential factors in the OPDP model.

Considering the current world economic environment and its prospects, we project that electricity consumption in China will sustain a 2% average yearly increase for the next 10 years. Now that electricity consumed in 2020 is predicted to be 6362.50 TW·h (China Electricity Council, 2020), we project that electricity consumed in 2021 will be 6916.3 TW·h and 9012.72 TW·h in 2030 as shown in Figure 4. Yu and Guo (2019) demonstrated that the cumulative proportion of Sub-C, Super-C and USC coal-fired units is around 79.4% of total installed thermal power capacity, which is echoed by Figure 2B. Thus, we assume that 79.4% of the projected total thermal electricity volume is produced by the coal-fired units.

Concerning the assumed annual newly installed capacity, we made several realistic assumptions: 1) if the electricity elasticity ⁶ is 0.8, then the overall growth rate of newly installed capacity can be set at 4% per year; 2) the share of thermal power in the newly installed capacities will decrease substantially in the next 10 years. According to CEC (China Electricity Council, 2020), the non-fossil newly installed capacity in 2020 is projected to be 89 GW or over 75% of total installed capacity. In this paper, it is assumed that in the coming 10 years, the share of newly installed capacity of coal-fired units will decrease from 18% in 2020 to 1.5% in 2030, and the missing market share of thermal power will be gained by PV and Wind. These projections are shown in detail in Figure 4, the national newly installed capacity will increase from 113.57 GW in 2021 to 161.64 GW in 2030; the newly installed coal-fired units will decrease from 18.17 GW to 2.42 GW; PV and Wind are projected to increase from 62.12 GW in 2021 to 154.56 GW in 2030. What should be noted is that, in the Strategy for Energy Production and Consumption Revolution (2016–2030) ⁷ , it is required that renewables should constitute the majority of newly installed capacity in 2030. Our projection can satisfy the requirement since newly installed renewables take a share of more than 95.6% in 2030.

Based on the above analysis, we can derive reliable results in the OPDP model. As for the LCIA analysis, emission inventory data under different technical approaches for 1 kW·h electricity production are collected from existing literature (Liang et al., 2013; Celik et al., 2016; Siddiqui and Dincer, 2017), which mainly include the amount of emitted CO₂, SO₂, NOx, CH₄, heavy metals, etc. With the method of ReCiPe 2016, the emission inventory data is calculated as the data of midpoint and endpoint level impact categories. Subsequently, we can derive the human health damage cost, environmental damage cost and economic losses caused by rising temperatures by utilizing the monetization method.

Pertaining to the optimal decarbonization path planning, the initial derived results will be expressed in the form of electricity production volume for different trajectories. Then, through the respective utilization hours, we can convert the electricity into capacity. Actually, the annual utilization hours (AUH) of different electricity production techniques vary a lot. According to our investigation, the national overall AUH increased from 3,790 h in 2017 to 3,820 h in 2019. If we separate the overall AUH into thermal power AUH, PV AUH and Wind AUH, we can find that the thermal power AUH increase from 4,219 to 4,307 h, PV from 1,205 to 1,291 h and 1949 h–2083 h for Wind.

A unique phenomenon of “PV and Wind abandon” has appeared in northwest China over the past few years, which is disturbing to the power sector. However, with the ultra-high voltaic transmission project coming into production and the construction of flexible peak shaving ability, such abandoning will ease (Si et al., 2019). Thus, we made some forecasts on the AUH in the next 10 years: 4,200 h for general coal-fired power units, 1,200 h for PV and 2,000 h for Wind.

In a well-known report about the basis for futures and options market in 1985, four questions were raised to test whether there is a concrete basis for the derivative market: 1) the economic function, 2) co-movement with the spot market, 3) regulation tools’ abundance and 4) protection on investors’ rights. Here, we try to briefly analyze the basis for carbon futures trading in China based on this framework.

Generally, the economic functions of futures market mainly include hedging and price discovery (Daskalakis, 2018). According to the analysis shown in Section 2, we hold the view that as long as enough speculators participate in this market, the depth and liquidity of the futures market can be significantly improved, and either market efficiency or the pricing efficiency can be elevated. Given that the trading cost in the futures market is much lower than the spot market, hedgers (power producers in this study) can transfer the risk to speculators, then the economic functions can be realized. Some scholars put forward the idea that futures trading will not play a significant economic function in mature financial market (Xiao, 2020), for all available information is already incorporated into the spot price. Concerning the carbon futures market, it is relatively immature, so carbon futures trading is expected to play an important role in the realization of the economic function, which have been verified in the EU ETS (Rittler, 2012)).

Considering that the carbon futures product is much like financial futures, experience in China’s traditional derivative market can give a hint when researching the co-movement between carbon spot and carbon futures (Su and Xie, 2017). Generally, it is considered that China’s financial futures market will enlarge the volatility of spot market in the short term, but financial derivatives can help to stabilize the spot market and therefore contribute to risk prevention in the long run (Agriculture, 1985). Thus, we can infer that, once the carbon futures market has been established, the market will potentially suffer temporary volatility, but it will ultimately benefit the carbon spot market, which is desired by the regulators.

Though a very limited variety of derivatives are traded in China’s financial derivative market, after several years’ operation, a set of regulation tools had been developed. For instance, there are limitations on positions and a special report scheme for influential investors, which mean that a relatively complete regulation framework has been created in China. Therefore, it can be expected that abundant regulation tools will be available for the carbon futures market.

To some extent, protection of investors’ rights is an obvious flaw in China’s financial market. Since the hierarchy of laws for China’s futures market is relatively low, investors’ rights cannot be protected well (Zhou and Li, 2019; Xiao, 2020). However, since the “Law for futures” is under enactment, protection of investor’s right will be significantly improved in the future.

According to the above analysis, we generally hold the opinion that in the course of time, the economic function, regulation of the market and protection of investors’ rights will significantly improve. As a result, introducing carbon futures trading should be a promising financial innovation in China.

Before discussing concerns about specific futures contracts, we should note that most positions held by the participants will be closed out prior to maturity, thus delivery is unusual (John, 2013), which means the actual influence of specific contracts is quite limited. Nonetheless, some brief discussions related to the contract concerns are made in this paper out of academic rigor.

Generally, the exact nature of the futures agreement will be specified in the contracts, for example, the underlier, contract size, delivery arrangements, etc. (Schwager and Etzkorn, 2016) listed 12 representative trading details for the specifications of futures products. Contract size varies for different futures, too big or too small is inappropriate for participants: investors who wish to hedge small positions will be unable to do so if the contract size is too small, and the cost of trading will be too large. The correct size can be ascertained by analyzing the likely users. Delivery places and delivery month will be determined in the delivery arrangements, occasionally, there will be alternatives for the delivery locations, which are determined by the Exchange. Futures contracts are for delivery in a specific month, take the carbon futures traded in European Climate Exchange as example, the contracts are listed on a quarterly expiry cycle (March, June, etc.) (Daskalakis et al., 2011). Price limits and positions limits exist in many futures contracts. The former is designed to constrain the over-movement induced by speculation, the latter is to prevent market manipulation (John, 2013).

The realization of expected hedging and the price discovery function is partly dependent on the specification of futures contracts. Specifically, realization of hedging is related to the contract size. The market should enable investors to hedge their positions, no matter how large or small the hedging positions are. Thus, with appropriate set of the contract sizes, the hedging function can be better realized. On the other hand, the expiry date will affect the evolution of futures prices, which has been proved by (Daskalakis, 2018), whose basic conclusion was that the longer the expiry date, the closer the futures price more likely to follow the spot price. Since the carbon futures have been traded in EU ETS for 15 years, reasonable delivery arrangements of China’s carbon futures contracts can be attained through following foreign experiences.

In general, the contract specifications have limited influences on the realization of carbon futures’ economic function. Furthermore, the above analysis also gives support to the previous conclusion that the essence of carbon futures trading can be viewed as locking in the executive carbon price, which is the basis for this study.