Systemic Risk in China’s Interbank Lending Market

We estimate an interbank lending distribution matrix, and then assume that the bankruptcy of a bank triggers a series of losses and other bank bankruptcies to establish an interbank bankruptcy chain network. We then analyze this network using the hyperlink-induced topic search (HITS) algorithm and identify the level of systemic risk. The empirical results show that there is no risk of systemic contagion in the interbank lending market in China. From the perspective of the lending market, China’s banking system is a network composed of core banks including the Bank of China and the Industrial and Commercial Bank of China, Level II banks including the Construction Bank of China, the Agricultural Bank of China, the Bank of Communications, the National Development Bank, and the Industrial Bank, and numerous Level III banks. Considering the influence of the entrance of nonbanking institutions into the interbank lending market, it is found that innovative online financial products have weakened interbank lending relationships to some extent and reduced the possibility of collective collapse caused by relation among banks in a crisis, and have thus facilitated risk diversification.


Introduction
were the first to study systemic risk in the interbank lending market using a quantitative method [1]. Degryse and Nguyen (2004) added time series and studied interbank systemic risk in Belgium based on annual data from 1993 to 2002. The results of their study show that systemic risk may change over time [2]. Toivanen (2009) analyzed systemic risk in the internal lending market in Finland during the period from 2005 to 2007 [3]. Allen and Gale (2000) proposed a systemic risk analysis using different structures [4]. Upper and Worms (2004) studied the relationship between the lending market structure and systemic risk and found that the risk in a complete market structure is lower than that in an incomplete market structure [5]. Boss (2006) et al. found that the network structure of the interbank lending market shows features of a small world [6]. Souma et al. (2003) identified the power-law distribution in the interbank lending market [7] [8]. Mistrulli (2007) conducted a contrastive analysis using real Italian data related to interbank lending and data estimated using the maximum entropy principle and found that the maximum entropy principle can reduce systemic risk to some extent [9]. Li and Li (2005) studied yearly data from 1996 to 2003 related to interbank lending in China and concluded that the Chinese banking system was not at risk of a systemic crisis in relation to the lending market [10]. Ma, Fan, and Cao (2007) summarized three forms of interbank systemic risk and analyzed the spread of systemic risk in the interbank lending market in China using the matrix method. The results of their study showed that the Bank of China (BOC) and the China Construction Bank (CCB) constituted the center of the Chinese banking network, and that there were relationships among all the other banks which have minor influence on the market structure [11]. The interbank deposits of non-depository financial institutions in China are increasing year by year. Thus, the relationships among the banks might change at some point, thereby affecting interbank systemic risk. Yu'E Bao, a money-market fund launched by Alipay, has injected more than 600 billion yuan as of March 2016, as well as a large number of derivative products, into the market, and this has had a significant influence on interbank relationships.
The HITS algorithm was developed by Jon Kleinberg (1997) to sort Web pages in order of importance [12], and Hu et al. (2012) used the HITS algorithm to evaluate risk rankings among banks [13]. In this paper, the HITS algorithm is used to calculate the vulnerability and contagion of individual banks so as to reflect the risks facing each bank. First, an estimation of an interbank lending distribution matrix is made, and then the bankruptcy of a bank is assumed, triggering a series of losses and bankruptcies to establish an interbank bankruptcy chain network. Finally, the network is analyzed using the HITS algorithm and the level of interbank systemic risk is evaluated. As routines, the sum of deposits in other banks and loans to other banks as recorded in the balance sheet are taken to represent each bank's assets in the interbank lending market, and the sum of deposits by other banks and loans from other banks as recorded in the balance sheet are taken to represent each bank's liabilities in the market. If the bank is failing or operating at a loss, its core capital will be treated as assets to cover the default loss. If the bank is insolvent, it will be deemed to have been bankrupted.

Matrix Estimation of Interbank Lending
Assume that there are N banks in the market and ij x is the ratio of bank i's de-posits in bank j to total interbank lending. ij x is unobservable, but the ratio of the total value of assets deposited by all other banks in bank i to total interbank Under market equilibrium, given certain constraints, the most reasonable solution is that which satisfies the principle of maximum entropy. The maximum entropy principle in relation to this problem is expressed mathematically as follows: A bank would not lend money to itself, so each diagonal is zero, namely, 0 ii x = .
The adjusted matrix should be consistent with the original matrix wherever possible. In general, the minimum cross-entropy principle should be followed: This problem may be solved using the RAS algorithm [14]:

Course of Risk Contagion
Assuming that a bank goes out of business, it transfers its losses to other banks through the interbank lending market so as to cause losses and even bankruptcies among other banks. The default loss ratio is θ and the repayment capital is i c . In the event that the first round of contagion starts when

The HITS Algorithm
The HITS algorithm was developed by Jon Kleinberg to rank Web pages in order of importance. The authority score (a) and hub score (h) of a Web page are the core components of this algorithm. The former focuses on the quality of the Web page [16], while the latter reflects the quality of the linkage [17]. The core principle of the HITS algorithm is that Web pages with a higher a value will be linked to more Web pages with a higher h value, while Web pages with a higher h value will be linked to more Web pages with a higher a value. The pseudo code of the HITS algorithm is as follows:

Data Processing
This study is based on the lending data and core capital data for 21 banks during the period from 2008 to 2015. The banks are listed in Appendix 1. The total assets of these banks account for more than 70% of total interbank assets, so these banks are a representative sample. There are also nonbanking institutions involved in the lending market, so the net amount of interbank lending is not zero, the balance reflecting the activities of the nonbanking institutions. In accordance with the rules of the financial industry, a bank will give priority to internal lending in the case of illiquidity. The maximum interbank lending scale is accordingly the sum of interbank lending.
Yu'E Bao is a service for individuals' fund payment with balance. The transfer of funds to Yu'E Bao enables the purchase of relevant financial products from both the Yu'E Bao fund and other institutions. Fund management companies place most of the funds under their control into the interbank lending market and mainly trade with 29 banks including policy-oriented banks, the four major state-owned banks, and joint-stock banks, i.e. basically the same banks that comprise the sample used in this study. Yu'E Bao lends money but never borrows, so it cannot be deemed a bank, and thus it cannot be included in the matrix of the 21 banks. Considering that, in the absence of other financing channels, the banks must depend on more frequent interbank lending to make up any shortfall, and thus the scale of lending will increase if Yu'E Bao is excluded, the following steps are taken to process the data (see Table 1

Results
Three aspects of interbank systemic risk need to be considered: the a and h values; the source of contagion, the number of bankrupted banks, and the ratio of core capital losses to total losses; and the critical value of bankruptcy.

a and h Values
The a value represents the degree of contagion of banks, while the h value represents the number of sources of contagion and contagiousness. The stronger contagiousness is, the more important the bank in the market.

Number of Sources of Contagion, Number of Bankrupted Banks, and Ratio of Core Capital Losses
The number of sources of contagion increased at first, then decreased, then increased again before finally decreasing again during the period from 2008 to 2015, as shown in Figure 1.
As shown in Figure 2, the number of closed banks initially increased and then decreased during the period from 2008 to 2015. The ratio of core capital losses to total losses slowly increased and then slowly decreased during the same period.

Critical Value of Bankruptcy
As shown in Figure    We acknowledge that this research has some deficiencies. First, lending interbank is only part of the banking business. In the event of the systemic crisis occurs, the bank is led into insolvency not only because of the mutual influence of the lending interbank business, but also the correlation of the portfolio of assets held by each bank. Second, Like attracts like is certainly in lending interbank business, a big bank prefer to do business with big banks. So the average distribution hypothesis of the maximum entropy principle is not reasonable. These deficiencies will underestimate the actual risk.