Environmental Science and Pollution Research https://doi.org/10.1007/s11356-017-1035-6

RESEARCH ARTICLE

Analysis of the transmission characteristics of China’s carbon market transaction price volatility from the perspective of a complex network Jingjing Jia 1 & Huajiao Li 1,2,3

&

Jinsheng Zhou 1 & Meihui Jiang 1,2,3 & Di Dong 1,2,3

Received: 30 July 2017 / Accepted: 12 December 2017 # Springer-Verlag GmbH Germany, part of Springer Nature 2017

Abstract Research on the price fluctuation transmission of the carbon trading pilot market is of great significance for the establishment of China’s unified carbon market and its development in the future. In this paper, the carbon market transaction prices of Beijing, Shanghai, Tianjin, Shenzhen, and Guangdong were selected from December 29, 2013 to March 26, 2016, as sample data. Based on the view of the complex network theory, we construct a price fluctuation transmission network model of five pilot carbon markets in China, with the purposes of analyzing the topological features of this network, including point intensity, weighted clustering coefficient, betweenness centrality, and community structure, and elucidating the characteristics and transmission mechanism of price fluctuation in China’s five pilot cities. The results of point intensity and weighted clustering coefficient show that the carbon prices in the five markets remained unchanged and transmitted smoothly in general, and price fragmentation is serious; however, at some point, the price fluctuates with mass phenomena. The result of betweenness centrality reflects that a small number of price fluctuations can control the whole market carbon price transmission and price fluctuation evolves in an alternate manner. The study provides direction for the scientific management of the carbon price. Policy makers should take a positive role in promoting market activity, preventing the risks that may arise from mass trade and scientifically forecasting the volatility of trading prices, which will provide experience for the establishment of a unified carbon market in China. Keywords Carbon-trade price . Price fluctuation . Conducting rules . Complex network

Introduction Highlights • Applied the complex network theory to study price fluctuation transmission regularity. • The clustering coefficient is low, and there is no direct relationship between the clustering coefficient and node strength. • The more smoothly the carbon market prices synchronously transmit, the more likely the modality will act as the hub of the network. • The mode with large price fluctuation acts as the main intermediary in the network. Responsible editor: Philippe Garrigues * Huajiao Li [email protected] 1

School of Humanities and Economic Management, China University of Geosciences, Beijing 100083, China

2

Key Laboratory of Carrying Capacity Assessment for Resource and the Environment, Ministry of Land and Resources, Beijing 100083, China

3

Lab of Resources and Environmental Management, China University of Geosciences, Beijing 100083, China

Based on research (Ahammad 2001), carbon emission trading is internationally recognized as an effective carbon emission reduction mechanism. China, as one of the countries with the largest carbon emissions in the world, is actively striving to achieve the strategic goal of low-carbon development. Since June 2006, China has started carbon emission trading pilot markets (hereinafter referred to as the carbon market) in Shenzhen, Beijing, Tianjin, Shanghai, Guangdong, Chongqing, and Hubei provinces and plans to establish a unified national carbon market in 2017, which will replace the EU (European Union) emission trading system and will then become the world’s largest carbon market. In this context, research on the characteristics and laws within carbon emission trading price (hereinafter referred to as the carbon price) is conducive to establishing an effective and standardized carbon trading system and providing a decision-making basis for China’s unified carbon market regulation and management.

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The trading price fluctuations in the carbon market can reflect the scarcity and value of carbon resources. As an important means of effective allocation of carbon resources, carbon price fluctuations have been receiving increasing attention. Some scholars have performed empirical studies by using the Generalized Auto Regressive Conditional Heteroskedasticity (GARCH) model, stochastic equilibrium model, and multivariate model to study the characteristics and influencing factors of the European Carbon Emissions Trading System (EU ETC), which was established and has developed rapidly since 2005 (Alberola et al. 2008; Koopman et al. 2007; GarcíaMartos et al. 2013). The results show that the European Union Allowance (EUA) has a high correlation with the policy changes in the trading market and demonstrates both clustering and sustainability (Conrad et al. 2012). Based on the conduction effect between the energy market and the carbon market, it was determined that the fluctuation of energy prices such as that of crude oil has a different conduction effect on the carbon price (Hammoudeh et al. 2015). In the long run, there is a significant linear relationship between the two markets (Yu et al. 2015). Extreme weather has led to an increase in demand for coal and other energy sources as well as to a rise in carbon emissions, which has a significant impact on the carbon price (Liu and Chen 2013). There are also studies that demonstrate that asymmetric information in the carbon market reduces market efficiency and, to a certain extent, will cause fluctuations in spot prices (Chesney and Taschini 2008). According to studies on the factors influencing the carbon market price in China, it has been found that the trading price of the carbon market in Shenzhen is affected by the Euro exchange rate and the domestic oil price, which is less affected by the international carbon price (Guo 2015). As the carbon market is affected by different factors in different degrees, the carbon price in different markets has different characteristics. However, it is important to study the price volatility of the carbon market in China. In this paper, the carbon trading price volatility problem includes a combination of the fluctuations in the spot trading price of carbon quotas in different carbon markets and the evolution of the changes over time. The purpose of this study is to reveal the problems existing in the operation mechanism of the pilot carbon market through the transmission characteristics of price fluctuations. Previous research on price fluctuations and the transmission mechanism was mainly based on the price of commodities, and the price change of some products had direct or indirect influence on other commodity prices and even the entire price level through cost and competition (Liu et al. 2009). Some scholars used the econometric model, general equilibrium model, and input-output model to study the transmission effect of price

volatility from the perspective of the entire society or macroeconomy (Liu and Ren 2016; Ren et al. 2007; Zhang 2008). With the deepening of the application of complex network methods in the economic and social fields, these researchers have achieved initial results in price fluctuation and conduction. Complexity is usually described by the coarsening of symbols and symbol sequences. Combining the complex network and symbolic dynamics, some scholars focused on the study of the transmission of price volatility of financial products according to the coarse-grained method (Mantegna 1999; Kim et al. 2002; Huang et al. 2008). For example, the stock price data of different countries at different times are used to construct complex networks(Huang et al. 2009; Mantegna 1999) and to study the correlation of stock activity fluctuation based on the common network of Chinese fund companies (Li et al. 2014). Through the construction of international oil price fluctuations in the complex network and China’s industrial product price synchronous transmission complex network (Chen et al. 2010; Liu et al. 2013), some scholars analyzed the topological features of the related price fluctuation in order to reveal the inherent law of price fluctuation and conduction. For example, the relationship between the futures price and the spot price is abstracted as the corresponding symbol, and the corresponding complex network model is established. The linkage between the futures price and the spot price in the crude oil market has been studied (Gao et al. 2011) in order to provide a unique perspective for price forecasting and regulation. To summarize, due to the short start-up time of China’s carbon trading pilot market and the existing research rarely involved in the Chinese carbon market, the pilot market trading system is not perfect, and the carbon price is more affected by the local government quota policy, with each of these markets having its own characteristics. The existing analysis of the price fluctuations of the EU carbon trading system is not applicable to China’s carbon market. In terms of methodology, the analysis of the carbon market price volatility transmission by using complex network is hardly found. Based on the construction of the China Carbon Price Fluctuation Network, this paper analyzes the volatility transmission mechanism and effect of China’s carbon market transaction price and then provides a policy suggestion for the effective operation of China’s carbon market.

Methodology and data Data selection We selected the closing prices for trading days of carbon markets in Beijing, Shanghai, Tianjin, Shenzhen, and Guangdong from December 29, 2013 to March 26, 2016,

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as sample data. All the data comes from China Carbon Trading Network. The carbon markets in Chongqing and Hubei were launched in 2014, and, given the data quality, these data were not included in this study. Each market has five trading days per week, and we eventually obtained 735 sets of data (see Fig. 1). Figure 1 shows the price changes and change trends in carbon-trade price in the five carbon markets (Beijing, Shanghai, Tianjin, Shenzhen, and Guangdong). Their crests and troughs are not completely corresponding, and the fluctuation direction is rarely consistent at the same time, resulting in the fluctuation range being quite different. The transmissions of each moment were combined to form a non-linear, unstable complex system.

Methodology Construction of transmission network Through the coarse graining of the sample data, the five carbon-trade prices of carbon markets were abstracted into the corresponding symbols, and a directed complex network of price volatility transmission was constructed. The coarse graining process is an equally dividing procedure that equally divides the entire section system into limited sub-intervals. Then, a character string was assigned for each of the subintervals. Next, the entire section system was transferred into a sequence of symbols. Due to the omission of some details in sub-intervals and finitude of symbolic sequences, the coarse graining process was conducive to revealing the nature of the link between conduction and carbon price. Therefore, a time series sequence of each carbon market price change index was transferred into a corresponding symbol time series sequence. For a continuous carbon price time series sequence, we set Tt as the carbon price in the current period, while T(t-1) was set as the carbon price of the previous period. Thus, the price gap between two periods can be denoted as ΔT = Tt − T(t-1). ΔT > 0 represents the rise of carbon price, while ΔT < 0 represents the decline of the carbon price. ΔT = 0 means the carbon price Fig. 1 Carbon-trade prices in Beijing, Shanghai, Tianjin, Shenzhen, and Guangdong from December 29, 2013 to March 26, 2016

100 90 80 70 60 50 40 30 20 10 0

remains the same during the periods. The basic assumption of time series analysis is not taking into account of other factors. Although many factors can affect current price variation, in the paper, we only consider price fluctuation in the past as the factor of influencing the current price variation. Taking the carbon market in Beijing as an example, we define variables for each corresponding ΔT. Then, the variation sequence of carbon price (ΔT) can be denoted by the corresponding set of variables (Bi). 8 < P ðΔT > 0Þ ð1Þ Bi ¼ O ðΔT ¼ 0Þ : N ðΔT < 0Þ where P, O, and N respectively represent the following three scenarios of carbon price floating: rises, remains, and decreases in price. The variation of carbon trading price in the Beijing carbon market from December 26, 2013 to March 29, 2016, was calculated (Tt − T(t-1)) and transferred into the corresponding symbol sequence: Bt ¼ ðB1 ; B2 ; B3 ⋯ÞðBi ∈ðP; O; NÞÞ

ð2Þ

Similarly, we can calculate the variation of carbon trading price in the carbon markets in Shanghai (St), Tianjin (Jt), Shenzhen (Zt), and Guangdong (Gt). The corresponding symbols of each sequence are listed in Table 1. where Ht, Jt, Zt, and Gt∈(P,O,N). After the symbol processing, the carbon price matrix of the five carbon markets is set as Ft: 2

3 Bt 6 Ht 7 6 7 7 Ft ¼ 6 6 Jt 7 4 Zt 5 Gt

Shanghai Tianjin Shenzhen Guangdong Beijing

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Corresponding symbol sequences of five carbon markets

Beijing

Shanghai

Tianjin

Shenzhen (SZA—2013)

Guangdong

Bt-Bt-1 O

Ht-Ht-1 N

Jt-Jt-1 P

Zt-Zt-1 P

Gt-Gt-1 O

O P

O P

O N

O P

N O

O O

O P

N N

N P

P O

⋮

⋮

⋮

⋮

⋮

Network topological property

Then, we used parallel processes to transfer the time series sequence into the corresponding symbol sequence Dt: 2

3 Bt − Bt−1 6 Ht − Ht−1 7 6 7 7 Dt ¼ 6 6 Jt − Jt−1 7 4 Zt − Zt−1 5 Gt − Gt−1 2 3 2 3 O P 6 P 7 6N7 6 7 6 7 7 6 7 ¼6 6 O 7⋯6 P 7ðt ¼ 1; 2; 3; ⋯; 192Þ 4O5 4O5 N N

ð3Þ

According to the rise, remain, and decline characteristics of price variation, theoretically, there are 243 (=35) modalities of carbon trading price in the five carbon markets. Each price sequence represents the price modality of five carbon markets. The study of each modality’s change pattern and symbol synchronization can reveal the internal relationship of the modalities. The modalities can be represented as OOOOO, OOOOP, OOOPP, OOPPP, OPPPP, PPPPP, PPPPN, PPPNN, etc. The calculation results show that only 192 modalities exist in the calculated period. Additionally, 51 modalities do not appear in the calculated period. We then built the transmission network of carbon trading price fluctuation in five carbon markets. We set each modality as one node of the network. The directed edges, which indicate the trading order, are used to link the nodes. The number of paths that connect two nodes equals the weight of the directed edges of two nodes when there are multiple disjointed paths between them. Two nodes are considered as non-edge if the modality of two continuous periods remains the same (e.g., OOOOO → OOOOO). Therefore, the directed connection of the complex network is as follows: ONPPO → OOOOO → PPNPO → OONNO → OPNPO → ONOOO → POOPO → OPPOO…. The price fluctuation transmission network of connected modalities can then be established, as shown in Fig. 2.

The fluctuation of carbon price modality will reflect a change in the price system of the carbon market at some degree. Each node, which represents the modality of carbon trading prices, has a different importance. Based on the topological features, this paper analyzes the node intensity, intensity distribution, the clustering coefficient, and the betweenness centrality of the trading price volatility transmission network. First, the degree of the node in the carbon market trading price volatility transmission network reflects the number of modalities that have a transmission relationship with a certain price. The network node is divided into in- and out-degrees. The in-degree indicates that the price fluctuation modality is affected by the other modalities, while the out-degree indicates that the price fluctuation modality affects other modalities. In this paper, a directed weighted price transmission network is established to depict the price volatility of five carbon markets. Because the nodes are linked in accordance with time, the in-degree and out-degree of the nodes are equal except for the first and last nodes. To simplify this research, out-degrees were chosen as the research objects. There is weight information in an edgeweighted network that corresponds to the strength of the point in a non-weighted network. The strength of the point contains information of both the number of neighbor nodes and weights between the node and their neighbors. It is a comprehensive reflection of local information of the node. The appearance frequency of different modalities and conductivity intensity between modalities should be considered to measure the correlation between modalities. Hence, the vertex strength was calculated for statistical analysis. The point strength was defined as follows (Yook et al. 2001): S i ¼ ∑jϵRi wij

ð4Þ

where Ri represents the neighbor set of node i while wij represents the weight of node i and node j. We define the point intensity distribution as E(s): EðsÞ ¼

Xi R

ð5Þ

where R is the sum of the mode intensity while Xi is the node intensity. The point intensity and intensity distribution depict the correlation degree between the modalities of carbon trading prices in the five trading markets. A higher point intensity and intensity distribution mean the modality has a higher

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Fig. 2 Schematic diagram of the complex network of volatility of the carbon trading price of five carbon markets

possibility of occurring in the network and a more important position in the network. Then, we calculated the clustering coefficient of the nodes. The clustering coefficient of nodes represents the degree of correlation between adjacent nodes. We used this index to study the transmission regularities of price fluctuations in five carbon markets. In carbon markets, the price volatility transmission network is a weighted network. The edge weight is a similar weight. A larger value indicates a closer relationship between two points and a decreased distance between the two points.

Table 2

The weighted clustering coefficient is defined as follows (Barrat et al. 2004):   wij þ wik 1 ∑ aij ajk aki C ðiÞ ¼ si ðk i −1Þ j;k 2

ð6Þ

w

where Cw(i) is the weighted clustering coefficient; si is the point strength of node i; Ki is the degree of node i; wij and wik represent the weight of the edges of nodes (i,j) and (i,k), respectively; and aij, ajk, and aki represent whether nodes

Ranking of point strength and its distribution of carbon price transmission network nodes

Ranking Order

1

2

3

4

5

6

7

8

9

Nodes Weighted out-degree Weighted out-degree (%) Ranking order Nodes Weighted out-degree Weighted out-degree (%)

OOOOO 138 18.83 10 POPPO 7 0.95

ONOOO 29 3.96 11 PONNN 7 0.95

OPOOO 26 3.55 12 POPNN 7 0.95

OOOON 12 1.64 13 NONPN 7 0.95

OOPPO 11 1.50 14 OOONO 7 0.95

OOOOP 11 1.50 15 OONNO 6 0.82

OOPNO 8 1.09 16 OONOO 6 0.82

PPNPO 7 0.95 … …

NOOOO 7 0.95 192 PNOOP 0 0

…

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800

3

600

2.5

lg LE(S)

400

LE(S)

Fig. 3 Relationship between point strength and integrated intensity. a Correlation of point strength and integrated intensity. b Regression analysis of logarithmic point strength and the integrated intensity’s logarithm

200

0

50

100

1

0.5 0

- 400

(a)

y = -0.4109x + 2.8806 R² = 0.8633

1

0 - 200

2 1.5

0

0.5

1

1.5

2

2.5

S

lg k

Correlation of point strength and integrated intensity

(b) Regression analysis of logarithmic point strength and the integrated intensity’s logarithm

(i,j,k) from a triangle. A value of 1 indicates that a triangle is formed, while a value of 0 indicates that the three nodes do not constitute a triangle. According to Eq. 6, a larger value of the weighted clustering coefficient indicates a closer relationship between two nodes and a shorter cycle of price volatility transmission. Moreover, the betweenness centrality of nodes is defined as the proportion of the number of shortest paths to all paths, and it reflects the impact of certain nodes’ influence on connection paths of any two nodes in the network. If a node is lost, the connectivity between nodes will be lost. For the five carbon market transaction price volatility transmission networks, the betweenness centrality can be used to measure each modality’s position in the topology structure in the network. To obtain a better understanding of the change of the carbon trading price and to discover the vital period in price volatility transmission, important nodes in the network were studied. Furthermore, the evolution trend of the entire network and the prediction of carbon price were solved by focusing on important nodes. The betweenness centrality of the network can be defined as follows (Zhou et al. 2008): ck ði; jÞ fk ¼ cði; jÞ

the edges of the path. Ck is the number of paths that pass through the intermediate node K. The intermediary centrality of fk is the sum of all nodes, fk(i,j) (Zhou et al. 2008): f k ¼ f k ði; jÞ ¼ ∑ði; jÞ f k ði; jÞ ¼ ∑ði; jÞ

ck ði; jÞ cði; jÞ

ð8Þ

Finally, the carbon market trading price volatility transmission network is divided by communities, and the price transmission ability is calculated to reflect the community characteristics of the network. The community in the complex network is defined as a sub-network with high node density, but the connection degree between these sub-networks is relatively low (Mucha et al. 2010). Scholars (Blondel et al. 2008) provide a method to divide communities effectively through keep merging nodes to get the optimal Q. On the basis of the method, in order to calculate the transmission ability between communities, TP → Q is defined as the price transmission ability from community P to community Q (Gao et al. 2014): T P→Q ¼ ∑i∈P; j∈Q Wi→ j ðP ¼ 1; 2; 3; ⋯k; Q ¼ 1; 2; 3; ⋯k:Þ ð9Þ

ð7Þ

where c(i,j) is the total number of the shortest paths between nodes (i,j). The length of the path is the sum of the weights of

where w i → j represents the weight between node i and node j, where node i belongs to community P and node j belongs to community Q. k is the number of communities

2.5

Fig. 4 Relationship between point strength (S) and ranking order (K)

2

y = -0.758x + 1.7895 R² = 0.8802

lg S

1.5 1 0.5 0

0

0.5

1

1.5

lg k

2

2.5

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(a)

(c)

(b)

Node OOOOO network structure

Node ONOOO network structure

Node OPOOO network structure

Fig. 5 Network structure of nodes OOOOO, ONOOO, and OPOOO. a Node OOOOO network structure. b Node ONOOO network structure. c Node OPOOO network structure

Table 3

Weight and weight distribution of nodes of OOOOO, ONOOO, and OPOOO

Node (modality)

OOOOO

Target Weight Weight (%)

OOOOO 57 41.30

ONOOO ONOOO 9 6.52

OPOOO 8 5.79

OOOOO 5 17.24

OPOOO ONOOO 4 13.79

OPOOO 4 13.79

OOOOO 6 23.77

OPOOO 4 15.38

ONOOO 2 7.69

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140

177

142

392

452

196

181

192

199

156

O

156 P

shanghai

anjin

N C

beijing

422

354

346

shenzheng guangdong

Fig. 6 Schematic diagram of days with different changes in trading price (O, P, and N)

in the network. The value is larger when the transmission ability has a stronger preference. And the effect of the transmission ability of community P on the whole network, TP is defined as follows: T P ¼ ∑kQ¼1 TP→Q

ð10Þ

Results and discussion Point strength and distribution The point strength and distribution of each node (price fluctuation mode) in the carbon price transmission network are shown in Table 2. Figure 3a shows the correlation of point strength and integrated intensity E (m). The logarithms of point strength and integrated intensity were calculated. Figure 4b shows the regression analysis of logarithmic point strength and the integrated intensity’s logarithm. The regression equation is y = − 0.410x + 2.880, and the regression coefficient is 0.863, which indicates that the logarithmic point strength and the integrated intensity’s logarithm are highly correlated. The point strength was sorted from high to low; the logarithm of the point strength was calculated, and the order was ranked. Then, the regression analysis was performed (see Fig. 4). The regression equation is y = − 0.758x + 1.789, and the regression coefficient is 0.880, which indicates that the logarithmic point strength and corresponding ranking order’s logarithm are highly correlated. Table 4

1.1 1.05 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -0.05 -0.1 0

y = -0.0009x + 0.106 R² = 0.0038

20

40

60

80

100

120

140

160

K

Fig. 7 Correlation of clustering coefficient and point strength

We can conclude that the point strength of nodes of the price volatility transmission network is highly correlated with integrated intensity and the ranking order. The result shows that there is a high occurrence possibility of high fluctuated price modalities and a low occurrence possibility of low fluctuated price modalities over a long period. The result reveals the nature of dynamic characteristics of the carbon price volatility transmission. Nodes OOOOO (prices of carbon emission right in five markets did not changed), OPOOO (price in Shanghai market decreased and prices of other four markets remained the same), and ONOOO (price in Shanghai market increased and price of other markets did not change) take a vital position in the price volatility transmission network and have a large influence on the network. These three nodes also transmit to each other frequently, which is the characteristic of the network. Figure 5 and Table 4 show the network structure, weight, and weight distribution of three nodes. Table 3 shows that the stable carbon trading price in five carbon markets is transmitted more smoothly. The numbers of days in which the trading price did not change in Beijing, Shanghai, Tianjin, Shenzhen, and Guangdong were 392 days (53.41%), 452 days (61.58%), 346 days (47.14%), 354 days (42.23%), and 422 days (57.49%), respectively (within the entire research period of 734 days) (Fig. 6).

Clustering coefficient and distribution of nodes in carbon trading price volatility transmission network

Ranking order

1

2

3

4

5

6

7

8

9

Nodes Clustering coefficient Proportion/% Degree Ranking order Nodes Clustering coefficient Proportion/% Degree

POPON 1 0.0510 1 10 NNPPN 0.5 0.0255 1

NOPOO 0.5833 0.0298 3 11 OPPPP 0.5 0.0255 1

ONNPP 0.5 0.0255 1 12 OPNNP 0.5 0.0255 1

NNNNP 0.5 0.0255 1 13 PNONN 0.5 0.0255 1

PNPNP 0.5 0.0255 1 14 POOPP 0.5 0.0255 2

NPNPN 0.5 0.0255 1 15 NPPON 0.5 0.0255 1

NPOPO 0.5 0.0255 1 16 PNPOO 0.3333 0.0170 1

OPNNN 0.5 0.0255 1 … … … … …

NNPPN 0.5 0.0255 1 192 PNOOP 0 0 0

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0.15 0.1 0.05 0 -0.05 -0.1 -0.15

0.4 0.2 0 -0.2 -0.4

Beijing

Shanghai

0.15 0.1 0.05 0 -0.05 -0.1 -0.15

Tianjin

0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2

Shenzhen Guangdong Fig. 8 30-day trading price of five carbon markets before the performance period in 2014

Furthermore, the price changes of nodes OPOOO and ONOOO (BP^ and BN^ appeared, respectively) only exist in the carbon market in Shanghai. This result indicates that the carbon trading price in the Shanghai carbon market is not synchronized with the other four trading markets, which is caused by the completely established market policies and regulations, diversification of transaction, smooth offset mechanism, and active CCER trading in the Shanghai carbon market.

Analysis of clustering coefficient The clustering coefficient of carbon trading price volatility transmission network was calculated (see Table 4). The result Table 5 Mediation centricity value and proportion of partial nodes

shows that the average clustering coefficient of the nodes is 0.11, which indicates that the collectivization degree of the network is low. Moreover, 120 nodes in this network have non-zero weighted clustering coefficients, which indicate that these nodes have connections with adjacent nodes and formed 120 small clusters. Furthermore, the cumulative distribution of the top 22 nodes reached 50.61%, which indicates that the 11.46% of the total nodes have more than half of the entire network’s intermediary function. Those 22 nodes have a tight connection with their adjacent but smaller scale nodes. The change of those 22 nodes will affect the modalities of adjacent nodes strongly. The correlation of clustering coefficient and point strength was then analyzed (see Fig. 7). A higher clustering coefficient

Ranking

Node

fk

fk (%)

Ranking

Node

fk

fk (%)

1 2 3 4 5 6 7 8 9 10 11

OOOOO ONOOO OPOOO OOOOP PONNN OOPPO OOOON NONOP PPNPN ONPPO OONNO

24,747.2706 3681.4518 3498.2631 1849.8064 1585.1604 1467.9557 1371.1629 1347.6208 1284.5899 1113.2287 1111.3588

26.0866 3.8807 3.6876 1.9499 1.6709 1.5474 1.4454 1.4206 1.3541 1.1735 1.1715

12 13 14 15 16 17 18 19 20 … 192

OOONO POPNN NPPPP PNNNP NONPN POPPO OONOO OONPN PPPPO … PNOOP

1073.0612 988.1052 977.8899 929.2272 921.3624 896.8704 889.2334 873.3096 865.8417 … 0

1.13113 1.0416 1.0308 0.9795 0.9712 0.9454 0.9373 0.9206 0.9127 … 0

Environ Sci Pollut Res 0 0

0.5

1

1.5

2

-0.5

lg fk

-1

y = -0.7081x - 1.1276 R² = 0.8901

Cluster

-1.5 -2 -2.5

r

Fig. 9 Correlation of ranking order and the mediation centricity

and point intensity reflect the importance of a node in a network. From Fig. 7, the clustering coefficient and point strength change simultaneously. The higher point strength corresponds to lower clustering coefficient, and the lower point strength corresponds to higher clustering coefficient. This result indicates that the node is not a random result and has a high complexity. Additionally, after further analyzing the symbol in the internal modality, it appears that the high appearance frequency of symbols BN^ and BP^ indicate that more BN^ and BP^ symbols exist in the system and the corresponding clustering coefficient is higher than other symbols. The modalities with more fluctuation in price have higher ability to group than other modalities. This explains the mass phenomenon in which the trading price of the carbon market would have high fluctuations in the performance period. Figure 8 shows the 30-day trading price of five carbon markets before the performance period in 2014. The fluctuation in carbon trading price was caused by larger trading volume before the performance period (May and June of each year). This characteristic will help us predict the mass phenomenon of carbon trading price. Moreover, there are no significant correlations between point strength and clustering coefficient.

Cluster Fig. 11 Distribution of community transmission ability

Betweenness centrality characteristic The betweenness centrality was calculated using Eq. 8. Table 5 shows the value and proportion of each node in the carbon trading price fluctuation network. The result shows that the fx of eight nodes (4.17% of total nodes) is zero, which indicates that there are no intermediary effects for price fluctuated conduction. Figure 10 shows the correlation of ranking order and the betweenness centrality logarithm of the top 49 nodes (25.52% of total nodes). These nodes’ betweenness centrality contains 73.18% of the total betweenness centrality. Figure 9 shows that the ranking order and the betweenness centrality logarithm are highly correlated. High betweenness centrality indicates more possibility for conduction. The study on the top 49 nodes reveals the regular pattern of carbon trading price fluctuate conduction. The 49 nodes can be divided into two groups. The first groups include nodes such as OOOOO, ONOOO, and OPOOO, which have high fx values and have large amounts of shortest paths passing near them. These are nodes with important

Fig. 10 Size of clusters and transmission ability

250 200 150 100 50 0 Total amount of nodes

1

2

3

4

5

6

7

8

9

10

41

17

19

13

11

12

21

17

22

18

Percentage of number of 21.47 8.90 9.95 6.81 5.76 6.28 10.99 8.90 11.52 9.42 nodes to the total Transmission ability Unit transmission ability

218.00 57.00 54.00 32.00 24.00 31.00 60.00 34.00 52.00 38.00 5.32 3.35 2.84 2.46 2.18 2.58 2.86 2.00 2.36 2.11

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positions. The second groups are nodes such as PONNN (price in Beijing market increased, price in Shanghai market price remained unchanged, and others’ decreased), NONOP (prices in Beijing and Tianjin markets decreased, prices in Shanghai and Shenzhen markets remained unchanged, and price in Guangzhou market increased), and PPNPN (prices in Beijing, Shanghai, and Shenzhen markets increased and prices in Tianjin and Guangzhou markets decreased), which have low point strengths but high fx values. They are the intermediary nodes that can indicate the transition period when a large amount of low point strength nodes appear. Therefore, fluctuation situations will be predicted when the transition period appears. From the price fluctuation point of view, the higher the point strength is (more of the same symbol appears), the higher the betweenness centrality value will be. The smoothly conducted nodes are more likely to be the hub node in the price fluctuation conduction network. Once lose these nodes, there will be a large impact on the whole network when the prices decrease.

preference. The characteristics of the network provide a scientific basis for the establishment of early warning mechanism of carbon market price risk.

Distribution of community price fluctuation transmission ability

(1) In this transmission network, the three modes of OOOOO, ONOOO, and OPOOO play important roles in the change of price transmission. Most modes have the tendency to transform to these three modes accordingly, or the probability that these modes transform into the others is very large. This feature fully reflects the common characteristics of the five carbon markets that the market transactions are not active enough and the price in most cases is stable. The price fluctuation of Shanghai’s carbon market is not synchronized with the other four markets. In the important models, the asynchronous features are more prominent. (2) In the carbon market, the clustering coefficient is low, and there is no direct relationship between the node clustering coefficient and node strength. On the one hand, the regional characteristics of the carbon market are affected by the regional policy, the emission reduction targets, the initial allocation of carbon emission rights, local trading rules, etc., resulting in trading platforms with limited size and carbon market transaction price being too scattered, which is not conducive to forming national carbon price signals. On the other hand, there is a large price fluctuation of mass characteristics in the performance period, increasing the risk in the carbon market. (3) In the carbon market, a small number of price fluctuation modalities play a pivotal and mediating role in network modal transformation. Among them, the more smoothly the five market prices synchronously transmit, the more likely the modality will act as the hub of the network. The mode with large price fluctuation, which is not the hub in the transmission between price modes, acts as the main intermediary in the network and reveals the

The China carbon market trading price volatility transmission network is divided into ten communities. The size of communities and transmission abilities between communities are shown in Fig. 10. The results show that the transmission abilities within each community are the strongest in the carbon market trading price volatility transmission network, which is the diagonal of Fig. 11. The result is consistent with the concept that nodes within the same community have higher degree of connection relative to nodes which are not divided into the same community. It proves that the community division is effective. Among the ten communities, community 1 contains 41 different modalities. Its transmission ability is 218 and the unit transmission ability is 5.3170, which is much higher than that of the other nine communities. Among the other nine communities, their transmission abilities and unit transmission abilities are relatively weak and presented as staircase distribution. In terms of the transmission ability among communities, cluster 1 has the strongest ability of transferring the fluctuation to others, and others have a stronger ability of transferring to cluster 1. It indicates that cluster 1 has a large influence on the price fluctuation transmission of the whole network. Other communities have lower transmission abilities. Some communities have only a one-way transmission, and some others do not have a transmission relationship. For example, the transmission ability between cluster 5 and cluster 6 is zero. In addition, the ability of transmitting from other nine communities to community 1 is higher than that of transmitting to other communities, indicating that the transmission direction has a

Conclusions and policy implications Conclusions In this paper, topological features, such as point intensity and intensity distribution, clustering coefficient, and betweenness centrality, are calculated and analyzed. The results show that the five carbon markets are relatively independent during the policy and market start-up period, and the trading price of each carbon market has unique operational characteristics. However, the transmission of price fluctuations is not an unrelated stochastic process, and discerning these vertices is helpful for us to understand fluctuation regularity and information transmission of the carbon market, thus further revealing the operation problems of carbon markets in China.

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alternating regularity of the five market price fluctuation modes. (4) The distribution of the price fluctuation transmission ability among communities reflects that the community effect exist and at the same time further explores the regularity of price fluctuation transmission in China’s carbon market. Firstly, the ability of transmission within communities is stronger than the ability of transmission among communities, which proves that the division of communities in the network is effective. Secondly, among ten communities, one community has the strongest transmission ability and the others have much lower transmission abilities. The preference of transmitting to the community with strongest transmission ability exists. Also, even communities with weak transmission abilities have preferences of transmitting to certain communities. For example, in Fig. 11, we can see that community 3 has the preference of transmitting to community 2 and community 4 and barely can transmit to other communities. The result illustrates that, to avoid bringing risk to other communities, the price modalities within the community with the strongest transmission ability should be monitored closely. Also, the transmitting preference of each community needs to be examined as the preference provides a clear direction for studying the risk control of price fluctuation transmission.

Policy implications In view of the structural characteristics of the five pilot carbon markets in China, we propose the following suggestions. (1) When the carbon market price is not active, we must first consider the influencing factors behind the phenomenon, such as the carbon spot trading mode, pricing and delivery of the restrictions on the degree of market transactions, the appropriateness of government’s quotas, rationality of allowing investment institutions to enter the system, the degree of emphasis on carbon trading, and investors’ expectations of rising prices and trading profits. In addition, it is necessary to improve the liquidity of the carbon market in China by developing carbon finance products such as carbon futures and improving the price mechanism of the carbon market by means of a price discovery function within carbon quota futures and the impact on carbon quota spot price. (2) The loose regional carbon market structure allows the carbon markets of various regions to design carbon market elements according to their own economic structure and local policies. Due to inconsistencies in the distribution of carbon quotas and different transaction rules among those markets, fragmentation of different pilot

market products exists. Therefore, a national unified carbon market should be built as soon as possible to improve and unify the various mechanisms of market transactions. But at the same time, the policy makers must take into account of social differences in regional economic development, industrial structure, energy consumption and emission reduction capacity, etc. They should learn from the EU carbon trading system (EU ETS) about the regional differential emission quota allocation measures and increase the liquidity and fairness of the carbon market, for the purpose of optimizing the carbon market price formation mechanism. (3) We should continue to study how to control the dominant node in order to control the entire carbon market price fluctuations in the evolution of the transmission network. Also, we need to do research on the nodes with higher betweenness centrality to study the process of carbon price fluctuations transmission. Thus, this method could help find the important links in the fluctuation of carbon trading prices, reveal the precursory law of alternating prices, scientifically determine whether the carbon market is in a transitional period, and forecast the fluctuation and transmission of carbon trading price. (4) Based on the regularity of price fluctuation transmission in China’s carbon market, establishing a supervision mechanism and monitoring the effect of local price fluctuations on the whole carbon market in terms of the degree and direction are needed. The mechanism can prevent the market risk caused by local price fluctuation, and finally, the carbon market can achieve stable and healthy development. For the data limitation, the results of this study in explaining the volatility of actual carbon market trading prices lack depth. Many issues, such as how to establish the relationship between price volatility and external factors, need to be further studied in the future.

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