417 research outputs found
Scale free effects in world currency exchange network
A large collection of daily time series for 60 world currencies' exchange
rates is considered. The correlation matrices are calculated and the
corresponding Minimal Spanning Tree (MST) graphs are constructed for each of
those currencies used as reference for the remaining ones. It is shown that
multiplicity of the MST graphs' nodes to a good approximation develops a power
like, scale free distribution with the scaling exponent similar as for several
other complex systems studied so far. Furthermore, quantitative arguments in
favor of the hierarchical organization of the world currency exchange network
are provided by relating the structure of the above MST graphs and their
scaling exponents to those that are derived from an exactly solvable
hierarchical network model. A special status of the USD during the period
considered can be attributed to some departures of the MST features, when this
currency (or some other tied to it) is used as reference, from characteristics
typical to such a hierarchical clustering of nodes towards those that
correspond to the random graphs. Even though in general the basic structure of
the MST is robust with respect to changing the reference currency some trace of
a systematic transition from somewhat dispersed -- like the USD case -- towards
more compact MST topology can be observed when correlations increase.Comment: Eur. Phys. J. B (2008) in pres
World currency exchange rate cross-correlations
World currency network constitutes one of the most complex structures that is
associated with the contemporary civilization. On a way towards quantifying its
characteristics we study the cross correlations in changes of the daily foreign
exchange rates within the basket of 60 currencies in the period December 1998
-- May 2005. Such a dynamics turns out to predominantly involve one outstanding
eigenvalue of the correlation matrix. The magnitude of this eigenvalue depends
however crucially on which currency is used as a base currency for the
remaining ones. Most prominent it looks from the perspective of a peripheral
currency. This largest eigenvalue is seen to systematically decrease and thus
the structure of correlations becomes more heterogeneous, when more significant
currencies are used as reference. An extreme case in this later respect is the
USD in the period considered. Besides providing further insight into subtle
nature of complexity, these observations point to a formal procedure that in
general can be used for practical purposes of measuring the relative currencies
significance on various time horizons.Comment: 4 pages, 3 figures, LaTe
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