Similarity and heterogeneity of price dynamics across China's regional carbon markets: A visibility graph network approach

Similarity and heterogeneity analysis of price dynamics across the region provide experiences for China's national carbon emission trading scheme. This study examines the dynamic behavior of carbon prices from the visibility graph network point of view, notably introducing the Jaccard coefficient to measure the similarity. By mapping daily carbon trading prices onto visibility graph networks, we analyze the characteristics of the carbon prices by topological measures of the networks. For the next step, we evaluate the similarity between pilots by the Jaccard similarity coefficient of the constructed visibility graph networks. Consequently, we cluster the pilots based on topology measures of the networks. Results show that the seven carbon markets in China have different patterns of similarity in visibility network properties: They are all small-world networks and are scale-free except for Chongqing pilot. Only Hubei and Shenzhen pilots are assortative, indicating a weak degree of market efficiency. At the same time, the two pilots have the highest value of Jaccard similarity coefficients and Shenzhen pilot presents the highest similarity to the supposed integrated market. According to the structure measures of the networks, the pilots are clustered into four groups which can be seen as sub-markets. Findings in this study indicate that inequalities across those groups should be sufficiently considered in the future national carbon market with particular emphasis on the Hubei pilot. Some sub-markets are suggested to be built according to the similarity in price dynamics.