We show, on the basis of our recently introduced stochastic model, that triangular arbitrage makes the auto-correlation function of foreign exchange rates negative in a short time scale.

We first show that there are in fact triangular arbitrage opportunities in the spot foreign exchange markets, analyzing the time dependence of the yen–dollar rate, the dollar–euro rate and the yen–euro rate. Next, we propose a model of foreign exchange rates with an interaction. The model...