We study the structure of the world foreign currency exchange (FX) market viewed as a network of interacting currencies. We analyse daily time series of FX data for a set of 60 currencies, including gold and other precious metals. From our data we construct a network with nodes respresenting exchange rates of a pair of currencies. We group all the possible exchange rates according to their base currency and study each group separately. For each group we calculate a correlation matrix and draw a corresponding minimal spanning tree (MST).
First, we look at the eigenspectrum of the correlation matrix and compare its structure for different base currencies. We find that the magnitude of the largest eigenvalue is strongly currency-dependent with the most characteristic values being observed for the peripheral currencies (high magnitudes) and the leading currency, USD (small magnitude). Since the largest eigenvalue describes the most collective factor of a market, the smaller is this eigenvalue, the more independent is the evolution of the underlying currency.
Next we calculate c.d.f. of the number of nodes with given multiplicity in the network. We observe that shape of this distribution depends on a base currency and that this dependence reflects the currency's position in the world financial system. For the majority of currencies we identify the scale-free behavior of c.d.f. with the scaling index smilar to its counterparts for other complex networks. However, for USD and its close satellites, the related network of MST nodes shows a significantly more random character.
Furthermore, we investigate the clustering structure of the analyzed networks. We employ a technique of filtering the correlation matrix by means of a moving threshold. We show that the majority of currencies belongs to a few clusters that either are formed around the most important currencies or are related to other geographical and economical factors. We also look deeper into a structure of currency network by considering weaker dependences that are better visible after eliminating nodes related to the leading currencies.
Finally, we analyze the temporal evolution of the network structure by dividing our data into short-period windows and comparing the results obtained for different windows. In this way we can inspect subtle changes in the network that can be related to some actual changes in the world economy structure. |