Network-based risk measurements for interbank systems
July
Network-based risk measurements for interbank systems
Yongli Li 0
Guanghe Liu 0
Paolo Pin
Filippo Radicchi, Indiana University,
UNITED STATES
0 School of Business Administration, Northeastern University , Shenyang , P.R.China , 2 Business School, Sun Yat-Sen University , Guangzhou , P.R.China , 3 Department of Decision Sciences, Innocenzo Gasparini Institute for Economic Research, and Bocconi Institute for Data Science and Analytics, University of Bocconi , Milano , Italy
This paper focuses on evaluating the systemic risk in interbank networks, proposing a series of measurements: risk distance, risk degree and m-order risk degree. The proposed measurements are formally proven to have good basic and extended properties that are able to reflect the effect of bank size, liability size, liability distribution, and the discount factor on the default risk, not only of a single bank, but also of the entire system. Additionally, the abovementioned properties and the relationship between risk distance and financial contagion indicate the rationality embodied in the proposed measurements. This paper also provides some implications on how to decrease or prevent the systemic risk in an interbank system.
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Data Availability Statement: All relevant data are
within the paper. Note that this paper mainly
focuses on the theoretical analysis and only some
numerical examples are provided. All the data
adopted in the numerical examples have been
contained and reported in our paper, and thus no
supporting information files are further needed in
our opinion.
1 Introduction
Since the Asian financial crisis of 1997, special attention has been paid to the role of the
growing interconnectedness between financial institutions among the many factors that affect
financial contagion [1,2]. Particularly after the global crisis of 2007?08, the architecture of
financial system building on the abovementioned interconnectedness was viewed as being
crucial for its central role in the financial contagion [3?5]. In fact, the abovementioned
interconnectedness between financial institutes constitutes the edge of a financial network and the
corresponding financial institutes are regarded as the nodes. Particularly, following numerous
studies in this field such as [6] and [7], we also focus on the interbank system that can be
considered as a fundamental structure for complex financial systems. Note that interbank
borrowing and loans, if any, form the abovementioned interconnectedness that link the
corresponding banks in the interbank network [8]. The network representation allows to study
propagation of failures: recalling the two mentioned financial crisis, for example, one bank's
insolvency may lead to the default cascades in the interbank network. Here, two periods are
considered: several banks are assumed to default in the first period and the set of these banks is
named initial default set, and then in the second period, some of the remaining banks may be
induced to default because of the existing borrowing and loan links. Facing this phenomenon,
we want to explore two problems. The first one is when one bank's insolvency occur, which
bank will be the next victim? The second one is which initial default set will cause the largest
Italian Ministry of Education Progetti di Rilevante
Interesse Nazionale (PRIN) Grant 2015592CTH (to
PP). The funders had no role in study design, data
collection and analysis, decision to publish, or
preparation of the manuscript.
amount of banks to default in the second period? This paper will inherit the idea of risk
propagation in networks [9] to cope with the two problems by way of providing a series of
convenient measurements.
More concretely, if the answer of the first question is known in advance of financial
contagion, we can inject liquidity into the more susceptive banks to avoid the spread of the crisis.
As the first contribution, we provide a new measurement named risk distance, with the
property that a shorter risk distance with the given initial default set means a higher likelihood of
default. Among a growing literature on risk analysis in financial networks, the harmonic
distance presented by [10] is noteworthy because it captures the susceptibility of each bank to the
distress of any other, so that it functions similarly to our proposed risk distance. However, the
risk distance that we define is different from the harmonic distance in two aspects: one is that
our risk distance considers the cash and marketable assets carried by the banks so that the
analysed banks can be heterogeneous, the other is that the risk distance defined here does not
assume that the initial default set only contains a single bank. As a result, we prove that our
newly proposed risk distance has several different properties with the famous harmonic
distance in the following parts of this paper. Overall, our risk distance is a node-level (or say
microscopic) indicator that reflects the default likelihood of the rema (...truncated)