Network analysis and systemic FX settlement risk
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José Henry León-Janampa
Abstract
A proposal for applying network analysis to a foreign exchange (FX) settlement system is considered. In particular, network centrality metrics are used to analyse payments of financial institutions which settle through CLS Bank (CLS). Network centrality metrics provide a way to study settlement members’ connectivity, obtain a sense of their payments evolution with time, and measure their network topology variability. The analysis shows that although the continuous link settlement (CLS) network structure can be approximated with a power law degree distribution for many trade days, this is not always the case. A network community detection algorithm is applied to the FX settlement network to explore relationships between communities and to detect classification patterns in the FX trading net payments. A metric called SinkRank is used to build a ranking of the most systemic settlement risk important financial institutions trading on the FX system, and to understand how the metric depends on network’s connectivity. Since network metrics do not fully explain the dynamics of the settlement process, the CLS’ settlement system is simulated to measure the contagion of unsettled trades and its spread among network members. The effect of settlement failure and contagion on the settlement members is also explored.
A Appendix
A.1 Pay-ins schedule and funding
The CLS Bank calculates the settlement member ith projected net position in each currency k (
This is done in order to bring the short projected net position within the short position limit. The CLS Bank further accelerates the pay-in requirements for each eligible currency in order to bring the projected aggregate short position at the SCTT within the ASPL. The CLS Bank calculates the expected aggregate short position
which is used to arrive at the revised cumulative pay-in amount
Next, I summarise some of the statistical metrics used to characterise the network.
A.2 Centrality measures
I describe a number of metrics used to characterise the network. Some of these measures provide metrics about individual nodes, whereas others return a value that applies only to the network as a whole. The first class of metrics includes simple quantities like number of nodes, number of edges, and average nodal degree. The second type of metrics relates to structural topics such as how nodes of different degrees tend to link each other or tend to cluster into relatively tightly connected sub regions of the network even while the network as a whole remains connected. To keep the paper self-contained, I review some of the centrality metrics useful to characterise the FX bilateral network.
Degree centrality.
The degree of a node is the number of links that a node. It measures how well connected the node is and not the criticality or importance of the node within the network. A useful way to get information about the network in terms of node characteristics is to plot a degree distribution of the network. In most cases networks tent to follow a power law distribution, which manifests itself by the presence of long tails.
Density.
It is defined by computing the ratio of the number of edges existing in the network over the total number of edges, where the total number of edges for an undirected network is equal to
Closeness centrality.
This metric measures how close a node is to every other node in the network [2]. It is calculated by taking the average of the shortest path lengths from one node to every other node in the network. It measures the importance of a node in the network; the lower the closeness centrality, the closer the nodes in the network to that specific node. It is a good indicator of how likely a failure of that node will spread to the other nodes.
Suppose
and the closeness
Eigenvector centrality.
This metric measures a node’s importance. It gives more weight to nodes that are connected to influential nodes. It is the basic idea behind Google’s page-rank metric, which ranks web pages. See [5] for the specific definition of the page-rank metric.
Connectivity or cohesion.
This metric computes the minimum number of nodes before the network becomes disconnected.
SinkRank.
SinkRank (SR) is a metric that measures how close a failing bank is to the other banks in the payment network. It is inspired in the closeness centrality measure.
To compute SinkRank of a node, we need to compute the inverse of the average number of payments or edges that need to be made for a unit of liquidity anywhere in the network to reach the failing node(sink node). The minimum possible average number of payments is 1, and thus,
Betweenness centrality.
Betweenness [2] is calculated using shortest paths, also called geodesics. The shortest path is calculated between each pair of nodes. The betweenness of a node or edge is the number of shortest paths that pass through it. If nodes or edges with high betweenness are deliberately removed from a network, the network will eventually become disconnected. The resilience of a network to a failure can be at least qualitatively assessed in this way. This idea is also used in Section 4 to find communities in the FX networks.
where
A.3 Modularity
Denote by
Let us calculate the expected number of links between the vertices if the links are placed at random. To do this, first consider a link attached to vertex i, which has degree
Combining (5) and (6), we find the difference between the actual and the expected number of links in a network having joint vertices of the same type. Then the fraction of that difference (5) minus (6) with the number of links m gives the modularity
Note:
This paper was written while the author was Director in the Quantitative Analysis Group at CLS Bank. The views and opinions expressed in this article are those of the author and do not necessarily reflect the official policy or position of CLS Bank.
Acknowledgements
I would like to thank H. Deo, A. Winters for useful discussions, also the two referees and editor for valuable comments on earlier versions of the paper.
References
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© 2017 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Special Issue: Monitoring Systemic Risk: Data, Models and Metrics
- Network analysis and systemic FX settlement risk
- The effects of leverage requirements and fire sales on financial contagion via asset liquidation strategies in financial networks
- On the effect of heterogeneity on flocking behavior and systemic risk
Artikel in diesem Heft
- Frontmatter
- Special Issue: Monitoring Systemic Risk: Data, Models and Metrics
- Network analysis and systemic FX settlement risk
- The effects of leverage requirements and fire sales on financial contagion via asset liquidation strategies in financial networks
- On the effect of heterogeneity on flocking behavior and systemic risk
