Figure 1.
Time series of credit default swaps throughout the credit crisis.
A plot of the CDS spread time series covering the financial crisis of 2008. The data ranges from January 2002 to December 2011. We can observe three market phases. Most CDS spreads peak around March 2009. The CDS prices are quoted in basis points (bp). The purpose of this plot is to highlight the market regimes, rather than the individual CDS spread evolution. Accordingly, the CDS spreads of all the financial entities are plotted here.
Figure 2.
The distribution of non-zero values of interdependence across the three periods.
(a) The counts in periods 2 and 3 are higher than in period 1. In addition, during periods 2 and 3 the distributions of have longer tails compared to period 1. (b) The distribution of non-zero values of trend reinforcement
across the three periods.
Figure 3.
Scatter plot of impacting versus vulnerability centrality.
Each institution in the CDS market is represented by three dots depending on the period (blue, green, red refers to period 1, 2, 3, respectively). The size of each node is determined by the average debt of a financial institution relative to the maximum average debt of a financial institution in a given period. Note that in this picture we present the non-normalised values of systemic impact and vulnerability, this exercise enables the comparison of node's centrality measures across periods. It can be seen that, while in period 1 most institutions are located between the two dotted lines, in period 2 and 3 many of them move to the top and bottom region. This means that ratio between the two centrality measures varies with the market phase. Few institutions of interest are labelled. For example, Bank of America (BOFA) remains in the same region across the three periods. With reference to the subsequent bow-tie construction used in Figure 4: The scatter plot is divided into 3 regions. Nodes in the region above the line correspond to the IN. Nodes in the region
correspond to the SCC. Nodes in the region
correspond to the OUT.
Figure 4.
The network of the CDS reference entities from period 2.
Each of the nodes represents a financial institution. Outgoing links from nodes that are in the top, or the IN of the bow-tie structure represent the estimated potential impact of a financial institution to its neighbours (see Materials and Methods). The nodes in the SCC are placed within a circle of radius one and centred at the origin. The distance of each node from the centre is Impacting centrality. The angle increases linearly from
to
. Thus, the closer a node is to the centre the higher is vulnerability-impacting centrality. Similarly, nodes in the OUT and IN are placed between angles
-
and
-
respectively. In addition, nodes in the OUT and IN are placed with an offset of 1.1 from the origin. With the bow-tie representation we are able to visually compare the centrality of a node
with node
. Also, with this visualisation we are able to extract a network of nodes that mostly impact the others, nodes that impact just as much as they get vulnerable, and nodes that are only vulnerable to the other nodes in the network. The size and the colour of the node reflects vulnerability-impacting centrality of a node (nodes with larger vulnerability-impacting centrality are in red). The colour assigned to links is based on where the links point to in the network. Links originating from IN to the SCC are in bright blue. Links originating in the SCC to nodes in the SCC are in green. Links that are originating in the SCC to the OUT are dull blue grey colour.
Figure 5.
Illustration of the -drawup methodology.
(a) The * represents local extrema that were not detected as drawups. The red-dots represent local maxima that were picked up as candidates for a -drawup. The green-dots represent the local minima that were picked up for a
-drawup. Compare the difference between the maxima and minima on days 5 and 6 respectively with
. Since,
greater than the difference, we iterate to the next set of local maxima and minima on days 7 and 8, keeping day 3 as the day from when we count a
-drawup (b) The plot highlights the
-drawup methodology applied to the time series of American International Group (AIG) and Merrill Lynch (MER).