Correlation patterns in foreign exchange markets

Abstract

The value of an asset in a financial market is given in terms of another asset known as numeraire. The dynamics of the value is non-stationary and hence, to quantify the relationships between different assets, one requires convenient measures such as the means and covariances of the respective log returns. Here, we develop transformation equations for these means and covariances when one changes the numeraire. The results are verified by a thorough empirical analysis capturing the dynamics of numerous assets in a foreign exchange market. We show that the partial correlations between pairs of assets are invariant under the change of the numeraire. This observable quantifies the relationship between two assets, while the influence of the rest is removed. As such the partial correlations uncover intriguing observations which may not be easily noticed in the ordinary correlation analysis.

Detecting correlations and triangular arbitrage opportunities in the Forex by means of multifractal detrended cross-correlations analysis

“…The Forex market determines currency exchange rates between any traded pair of currencies through a complex and nowadays mostly machine-driven automatic system of multiple type transactions among different kinds of buyers and sellers round-the-clock. Most recent works on uncovering patterns in foreign exchange markets include, but are not limited to, studies of lead-lag relationships [7], scaling relationships [8], multifractality and efficiency issues [9,10], partial correlations [11] or quote spreads in high-frequency trading [12].…”

The Impact of the Measure Used to Calculate the Distance between Exchange Rate Time Series on the Topological Structure of the Currency Network

“…Distances between time series vectors can also be determined using the Euclidean measure, Spearman's rank correlation coefficients, Kendall's coefficients, partial correlations, or more ambitiously using the copula functions, the Granger causality distance, the PCA distance, dynamic time warping (DTW) or entropy measures (e.g., Kullback-Leibler or Jensen-Shannon divergence). A good illustration of the use of the partial correlation coefficient to build a network are the works of Kenett et al (2010) [45] and Basnarkov et al (2019) [2]. The copula-based approach, which aims at including non-linear relationships in the analysis, was used by Marti et al (2016) [46].…”

“…They will then be compared among themselves and conclusions will be drawn regarding the impact of the distance measure used on the final result. In our research we will refer to the thesis of Basnarkov et al (2019) [2], which states that the strength of ordinary correlations is highly dependent on the choice of numeraire currency, while partial correlations are invariant in this aspect.…”

High-Dimensional Precision Matrix Estimation through GSOS with Application in the Foreign Exchange Market

“…We gather the data initially with the US dollar (USD) as numeraire and then, according to the initial data, calculate all currency exchange rates (for more detail, see [23,24]). After determining all exchange rates, using each of the 32 currencies as a numeraire, we compute the daily log returns of the remaining 31 currencies.…”