A dynamic network model for interbank market
Introduction
Interbank market permits liquidity exchanges among financial institutions through facilitating the allocation of the liquidity surplus to illiquid banks. Complex network relationships are formed through interbank lending, payment and settlement, discount and guarantee. On one hand, the complex debtor–creditor relationships between banks provide channels for interbank liquidity exchanges, but on the other hand, they also become potential paths for financial contagion, which may trigger the domino effect. For example, the US sub-prime mortgage crisis broke out in August 2007, resulting in large number of bank failures (such as Lehman Brothers, Washington Mutual Bank, Colombia Trust, etc.), which quickly evolved to a global financial crisis and greatly damaged the global financial system.
Complex network theory is an important tool for complex system modeling and its common topologies include Erdős–Rényi random graph [1], small world network [2], [3], scale-free network [4], etc. Multi-agents methods can be used to model and analyze the behavior of agents. Interbank market has shown a high degree of complexity and intelligence and owns a variety of network structures [5], [6] (such as money center structure, complete market and incomplete market, etc.).
There has been large number of empirical literature on interbank market network structure. Souma, Fujiwara, Aoyama [7] found that the Japanese business network had scale-free property through empirical results. The work of Boss, Elsinger, Summer et al. [8] showed that the Austrian interbank network followed power-law distribution, interbank liability network owned a community structure, a low clustering coefficient and a short average path length. The structure of Italian interbank market proved to be a random network, changed over time [9], and consisted of two communities, one mainly composed of large and foreign banks, the other composed of small banks [10]. Brazilian interbank network structure emerged as a weak community structure and with high heterogeneity [11]. Tabak, Cajueiro and Serra [12] constructed the Brazilian interbank network with minimum spanning tree method and they discovered that the private and foreign banks tended to form clusters within the network and that banks with different sizes were also strongly connected and tended to form clusters. Soramäki, Bech, Arnold et al. [13] found that the US interbank market network had a low average path length and low connectivity, and the degree distribution was scale free over a substantial range. Craig, Von Peter [14] developed a coreperiphery model and found evidence of tiering in the German banking system. Peltonen, Scheicher, Vuillemey [15] suggested the CDS network exhibited a “small world” structure and a scale-free degree distribution.
Recently, scientists tried to use simulation modeling methods to explore the formation mechanism of interbank market network structure. Wan, Chen, Liu [16] developed a growth network model to explain the phenomenon of two-power-law distribution of banking system. Inaoka, Takayasu, Shimizu et al. [17] proposed a procedure to construct a network structure from a set of records of transactions, which was followed by a power-law degree distribution. Li, He and Zhuang [18] introduced an interbank market network model based on interbank credit lending relationships and showed typical structural features such as a low clustering coefficient and a relatively short average path length, community structures, and dual power-law distribution of out-degree and in-degree.
Through the above analysis, we summarize the following disadvantages for current simulation models to construct a interbank market network: The structure of the interbank network constructed by current models is static, which does not change with bank dynamic behavior over time; Building processes of interbank market by the current models are relatively simple, usually by assuming the interbank market to be a particular network architecture, such as a random network, a small-world network or a scale-free network, which does not take the bank’s own behavioral characteristics (such as asset liabilities) into consideration. But empirical results have demonstrated that the actual interbank market network structure evolves over time [9], the establishment of an interbank lending relationship is associated with bank credit lending scales, banks with different credit lending scales tend to establish strong connections and easily form cluster structures [12]. In this paper, we build a dynamic bank balance sheet to describe the bank dynamic behavior and develop a model to construct interbank market network based on bank behaviors. Moreover, the evolution of the structure of interbank market network is analyzed. Finally, we investigate the effects of fluctuations of deposit and investment yield on the stability of the interbank market network.
The remainder of this paper is organized as followed. The interbank market network model is introduced in Section 2, simulation experiments and relative analysis are presented in Section 3, further discussions are made in Section 4, and conclusions are given in Section 5.
Section snippets
The model
In this paper, a directed graph is used to denote the interbank market, where the parameter represents the set of all of banks and the parameter is the collection of all credit links between banks. A directed edge exists between nodes , if and only if bank is the creditor of bank . We assume the number of total banks , denotes a collection composed of neighbors of bank , and matrix represents credit lending scales of banks, where denotes the
Simulation results
In this paper, we initialize the number of total banks in the interbank market , the power-law parameter [8]. According to the data of “China Financial Statistics Yearbook of 2014”, the ratio of initial deposits to the initial bank total assets is set as , the ratio of interbank borrowing and liquid assets to the bank total assets is set as , respectively. In accordance with the benchmark interest of Chinese commercial banks, we set
Discussion
The model developed in this paper presents an approach to construct dynamic interbank market network based on bank behaviors. We describe the ever-changing behaviors of banks with the evolving bank balance sheet. The interbank market network built by the model has scale-free and small world properties, which have been shown by empirical results. There may be some shortcomings for the proposed model. To simplify computation, we update deposits and bank external investment yield rate through
Conclusions
In this paper, we build a dynamic model for interbank market based on bank agents behavior and investigate the evolution features of network structure and the impact of shocks on the stability of the network. Simulation results demonstrate that interbank market is a small world network and cumulative degree probability follows power law distribution. With the increase of interbank credit lending risk preference, average shortest path length becomes shorter, which suggests improvement of
Acknowledgments
We would like to thank anonymous referees for their helpful comments. This work is supported by the National Natural Science Foundation of China (Nos. 71371051 and 71201023), the Fundamental Research Funds for the Central Universities, College Postgraduates Research Innovation Program of Jiangsu Province (KYZZ15_0067), Teaching and Research Program for Excellent Young Teachers of Southeast University (No. 2242015R30021), and Social Science Foundation of Jiangsu Province (No. 15GLC003).
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