Systemic risk from financial intermediaries (FIs) refers to a negative externality problem, which is rife with fallacy of composition-type errors. To ‘see’ why seemingly rational behaviour at the level of an individual FI contributes to system-wide instability is a non-trivial exercise, which requires holistic visualization and modelling techniques. Paradox of volatility inherent to market price-based measures of systemic risk has made bilateral balance sheet and off balance data between FIs and network analysis essential for systemic risk management. There is both a data and a skills gap in implementing large-scale data-driven multi-agent financial network models that can operationalize macro-prudential policy. Different designs for a Pigou-type systemic risk surcharge are discussed with special reference to the Markose eigen-pair method, which simultaneously determines the degree of instability of the network of financial flows of obligors and also the rank order in the centrality of FIs contributing to it.
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That is, the weight, pi,s, is the same for all networks with the same number of nodes and is given by pi,s= if i∈S. Here, |S| denotes the cardinality of a set S, where S is a subset of set of all nodes, N, and S includes the ith FI. The MSV is given by the formula: φiMSV(v(c(g(S))= Here, v is the value function, such as the system value-at- risk, of a connected subgraph, in our case here of financial liabilities between FIs, respectively denoted by c(g(S)) and v(c(g(S\i)) is the value function calculation done for the connected subnetwork without i. This is explained in Section 3.1 of Kirman et al.104.
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In general, the unconstrained case of (A.1) is used, ujq. That is, the indicator function that signifies only banks that fail at q no longer applies and we have a weighted sum of the impact of all j counterparty banks, j≠i in the second term.
This article has benefitted from discussions with Alistair Milne, Rosa Lastra, Patrick McGuire, Teressa Glasser, Michael Bennett, Liz Dixon, David Bholat, Ulrich Krüger and other participants at the Future of Regulatory Data and Systemic Risk Analytics, Bank of England Workshop, 17–18 January 2012. I am grateful for inputs from anonymous referees and from Dalwinder Singh, the Editor of the journal. All views, errors and omissions are mine and cannot be attributed to any of the institutions mentioned above.
The dynamics characterizing transmission of ‘infection’ in a financial networked system can be given by:
Here, we have an FI’s own metric of failure at q, which is given by u iq =(1−C iq /Ci0), where C iq /Ci0 is the ratio of capital at q and capital at initial date. The second term in (A.1) involves the losses from counterparties, j, that fail at q and these are denoted by an indicator function, which is set equal to 1. The sum of ‘infection rates’ defined by the sum of net liabilities of its j failed counterparties relative to its own capital is given by the term
In order for the eigen-pair stability analysis to be used, in matrix notation the dynamics of financial contagion takes the following form:114
Here, Θ′ is the transpose of the matrix in (1) with each element θ ij ′=θ ji and I is the identity matrix.
The system stability of (A.2) will be evaluated on the basis of the power iteration of the matrix Q. From (A.2), U q takes the form:
Markose33 shows how the stability of the system in (A.3) as q tends to infinity requires that the maximum eigenvalue, λmax, is less than the common threshold on capital, ρ.
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Markose, S. Systemic risk analytics: A data-driven multi-agent financial network (MAFN) approach. J Bank Regul 14, 285–305 (2013). https://doi.org/10.1057/jbr.2013.10
- systemic risk
- macro-prudential policy
- financial network
- agent-based modelling
- eigenvector centrality
- Pigou-type surcharge