Multiscale cross–correlations and triangular arbitrage opportunities in the Forex
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Multifractal Detrended Cross-Correlation methodology is applied to the foreign exchange (Forex) market. High frequency fluctuations of exchange rates of eight major world currencies over the period 2010–2018 are used to study cross-correlations. The currencies include the Australian dollar, Canadian dollar, Swiss franc, euro, British pound sterling, Japanese yen, New Zealand dollar and US dollar. Dominant multiscale cross–correlations between the exchange rates are found to typically occur on the level of small and medium size fluctuations. Hierarchical organization of ties between the exchange rates, formulated in terms of the dendrograms, are however more pronounced on the level of larger fluctuations. The cross–correlations are quantified to be stronger on average between those exchange rate pairs that are bound within triangular relation. Some pairs from outside the triangular relation are however identified to be exceptionally strongly correlated as compared to the average strength of correlations in this sector. This in particular applies to those exchange rates that involve the Australian and New Zealand dollars and reflects their economic relations. Significant events with impact on the Forex are shown to induce triangular arbitrage opportunities which at the same time reduce cross–correlations on the smallest time scales and act destructively on the multiscale organization of correlations. In the years 2010–2018 such instances took place in connection with the Swiss National Bank intervention and the weakening of British pound sterling accompanying the initiation of Brexit procedure.
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