توپولوژی بازار ارز خارجی با استفاده از روش ساختار سلسله مراتبی

This paper uses two physics derived hierarchical techniques, a minimal spanning tree and an ultrametric hierarchical tree, to extract a topological influence map for major currencies from the ultrametric distance matrix for 1995–2001. We find that these two techniques generate a defined and robust scale free network with meaningful taxonomy. The topology is shown to be robust with respect to method, to time horizon and is stable during market crises. This topology, appropriately used, gives a useful guide to determining the underlying economic or regional causal relationships for individual currencies and to understanding the dynamics of exchange rate price determination as part of a complex network.

Hierarchical structure methods are used in finance to ascertain the structure of asset price influences within a market. These methods use the synchronous correlation coefficient matrix of daily difference of log prices to quantify the pricing distance between assets in terms of the inherent hierarchical structure. This structure will give some indication of the taxonomy of an asset's portfolio, and can be used to generate an asset market's hierarchy. Two techniques will be used in this paper. The first technique is the creation of a minimal spanning tree (MST), which is a graph of a set of n elements of the arrangement of the nodes in an ultrametric space. MST has been shown to provide sound results for financial assets with the resultant taxonomy displaying meaningful clusters [1], [2], [3] and [4]. MST also helps to overcome the empirical problem of noise in a historical correlation matrix [5] and [6]. The second technique is the creation of an ultrametric hierarchical tree structure [6] and [7]. This technique gives a determination of the hierarchical structure of a network and is particularly useful for determining if hubs exist. The structure of asset price movements is extracted by use of a synchronous correlation coefficient matrix, AijAij, of daily difference of log prices. This matrix is transformed [8] by the equation below to get the ultrametric pricing distance between currencies. This metric is preferred to correlation as it fulfils the three axioms of a metric distance [1], View the MathML sourced(i,j)=2(1-Aij). Turn MathJax on The choice of clustering procedure is vital as it has more effect on the quality of clustering than does the choice of distance metric [9]. MST analysis uses the single-linkage clustering method which builds up clusters by starting with distinct objects and linking them based on similarity. The major issue with this method is that while it is robust for strongly clustered networks, it has a tendency to link poorly clustered groups into chains by successively joining them to their nearest neighbours [10]. These chains are non-robust to data variation, and thus MST is less robust for larger distances. The information obtained should thus be used with care and be combined with other techniques if possible. This paper will focus on the extraction of price influences rather than on determinants of market activity.

This paper has shown that hierarchical methods can be used to analysis foreign exchange price influences. The results show price determination in international currency markets displays sparse clustering. The network has a simple tree-like structure with a dominant spine. Underneath the predominant influence of the USD and the EMS, there are clear secondary relationships based on economic or regional factors. This topology was shown to be robust to time horizon and market crises. The paper also indicates that the transmission process for cascading shocks is primarily through the spine and then through links outside of that spine. The anomalous placement of the DEM within the Asian cluster, however, indicates that care is needed with regard to interpretation of results. This ambiguity, together with the known tendency of the single-linkage clustering method to generate unstable spurious linkages, means that MST results should always be handled with care, and used together with other methods when analysing network structure. Overall the results also provide an indication that the price determination structure of international currency markets is tree like and sparsely clustered. This implies dynamic behaviour related to complex networks can be applied to currency markets.