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Agent-based model with multi-level herding for complex financial systems.

Chen JJ, Tan L, Zheng B - Sci Rep (2015)

Bottom Line: Further, we propose methods to determine the key model parameters from historical market data, rather than from statistical fitting of the results.These properties are in agreement with the empirical ones.Our results quantitatively reveal that the multi-level herding is the microscopic generation mechanism of the sector structure, and provide new insight into the spatio-temporal interactions in financial systems at the microscopic level.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Physics, Zhejiang University, Hangzhou 310027, China [2] Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.

ABSTRACT
In complex financial systems, the sector structure and volatility clustering are respectively important features of the spatial and temporal correlations. However, the microscopic generation mechanism of the sector structure is not yet understood. Especially, how to produce these two features in one model remains challenging. We introduce a novel interaction mechanism, i.e., the multi-level herding, in constructing an agent-based model to investigate the sector structure combined with volatility clustering. According to the previous market performance, agents trade in groups, and their herding behavior comprises the herding at stock, sector and market levels. Further, we propose methods to determine the key model parameters from historical market data, rather than from statistical fitting of the results. From the simulation, we obtain the sector structure and volatility clustering, as well as the eigenvalue distribution of the cross-correlation matrix, for the New York and Hong Kong stock exchanges. These properties are in agreement with the empirical ones. Our results quantitatively reveal that the multi-level herding is the microscopic generation mechanism of the sector structure, and provide new insight into the spatio-temporal interactions in financial systems at the microscopic level.

No MeSH data available.


The absolute values of the eigenvector components ui(λ) corresponding to the three largest eigenvalues for the cross-correlation matrix C calculated from (a) the empirical data in the HKSE; (b) the simulated returns for the HKSE.Stocks are arranged according to business sectors separated by dashed lines. Sector (2) and (3) are composed of two business sectors, respectively (Methods). (1): Real Estate Development; (2): Conglomerates - Industrial Goods; (3): Basic Materials - Technology; (4): Services; (5): Consumer Goods.
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f4: The absolute values of the eigenvector components ui(λ) corresponding to the three largest eigenvalues for the cross-correlation matrix C calculated from (a) the empirical data in the HKSE; (b) the simulated returns for the HKSE.Stocks are arranged according to business sectors separated by dashed lines. Sector (2) and (3) are composed of two business sectors, respectively (Methods). (1): Real Estate Development; (2): Conglomerates - Industrial Goods; (3): Basic Materials - Technology; (4): Services; (5): Consumer Goods.

Mentions: To characterize the spacial structure, we first compute the equal-time cross-correlation matrix C122952, of which each element isHere represents the average over time t, and Cij measures the correlation between the returns of the i-th and j-th stocks. From the definition, C is a real symmetric matrix with Cii = 1, and the values of other elements Cij are in the interval [−1, 1]. The first, second and third largest eigenvalues of C are denoted by λ0, λ1 and λ2, respectively. Now we focus on the components ui(λ) of the eigenvector for the three largest eigenvalues. The empirical result of the NYSE is displayed in Fig. 3(a). For λ0, the components of the corresponding eigenvector are relatively uniform. The eigenvectors of λ1 and λ2 are dominated by sector (5) and sector (1) respectively, with the components significantly larger than those in other sectors. These features are reproduced in our simulation, and the results are shown in Fig. 3(b). The empirical result of the HKSE is displayed in Fig. 4(a). The eigenvectors of λ1 and λ2 are respectively dominated by sector (1) and sector (2), and these features are simulated by our model, shown in Fig. 4(b). For the HKSE, the scenario is somewhat complicated53, since a company in the HKSE usually runs various business. As a result, the components of the eigenvector of λ0 are not so uniform as those in the NYSE. The dominating sectors for λ1 and λ2 are less prominent, especially for λ2.


Agent-based model with multi-level herding for complex financial systems.

Chen JJ, Tan L, Zheng B - Sci Rep (2015)

The absolute values of the eigenvector components ui(λ) corresponding to the three largest eigenvalues for the cross-correlation matrix C calculated from (a) the empirical data in the HKSE; (b) the simulated returns for the HKSE.Stocks are arranged according to business sectors separated by dashed lines. Sector (2) and (3) are composed of two business sectors, respectively (Methods). (1): Real Estate Development; (2): Conglomerates - Industrial Goods; (3): Basic Materials - Technology; (4): Services; (5): Consumer Goods.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4323661&req=5

f4: The absolute values of the eigenvector components ui(λ) corresponding to the three largest eigenvalues for the cross-correlation matrix C calculated from (a) the empirical data in the HKSE; (b) the simulated returns for the HKSE.Stocks are arranged according to business sectors separated by dashed lines. Sector (2) and (3) are composed of two business sectors, respectively (Methods). (1): Real Estate Development; (2): Conglomerates - Industrial Goods; (3): Basic Materials - Technology; (4): Services; (5): Consumer Goods.
Mentions: To characterize the spacial structure, we first compute the equal-time cross-correlation matrix C122952, of which each element isHere represents the average over time t, and Cij measures the correlation between the returns of the i-th and j-th stocks. From the definition, C is a real symmetric matrix with Cii = 1, and the values of other elements Cij are in the interval [−1, 1]. The first, second and third largest eigenvalues of C are denoted by λ0, λ1 and λ2, respectively. Now we focus on the components ui(λ) of the eigenvector for the three largest eigenvalues. The empirical result of the NYSE is displayed in Fig. 3(a). For λ0, the components of the corresponding eigenvector are relatively uniform. The eigenvectors of λ1 and λ2 are dominated by sector (5) and sector (1) respectively, with the components significantly larger than those in other sectors. These features are reproduced in our simulation, and the results are shown in Fig. 3(b). The empirical result of the HKSE is displayed in Fig. 4(a). The eigenvectors of λ1 and λ2 are respectively dominated by sector (1) and sector (2), and these features are simulated by our model, shown in Fig. 4(b). For the HKSE, the scenario is somewhat complicated53, since a company in the HKSE usually runs various business. As a result, the components of the eigenvector of λ0 are not so uniform as those in the NYSE. The dominating sectors for λ1 and λ2 are less prominent, especially for λ2.

Bottom Line: Further, we propose methods to determine the key model parameters from historical market data, rather than from statistical fitting of the results.These properties are in agreement with the empirical ones.Our results quantitatively reveal that the multi-level herding is the microscopic generation mechanism of the sector structure, and provide new insight into the spatio-temporal interactions in financial systems at the microscopic level.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Physics, Zhejiang University, Hangzhou 310027, China [2] Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.

ABSTRACT
In complex financial systems, the sector structure and volatility clustering are respectively important features of the spatial and temporal correlations. However, the microscopic generation mechanism of the sector structure is not yet understood. Especially, how to produce these two features in one model remains challenging. We introduce a novel interaction mechanism, i.e., the multi-level herding, in constructing an agent-based model to investigate the sector structure combined with volatility clustering. According to the previous market performance, agents trade in groups, and their herding behavior comprises the herding at stock, sector and market levels. Further, we propose methods to determine the key model parameters from historical market data, rather than from statistical fitting of the results. From the simulation, we obtain the sector structure and volatility clustering, as well as the eigenvalue distribution of the cross-correlation matrix, for the New York and Hong Kong stock exchanges. These properties are in agreement with the empirical ones. Our results quantitatively reveal that the multi-level herding is the microscopic generation mechanism of the sector structure, and provide new insight into the spatio-temporal interactions in financial systems at the microscopic level.

No MeSH data available.