Triangular arbitrage as an interaction among foreign exchange rates
  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 includes effects of triangular arbitrage transactions as an interaction among three rates. The model explains the actual data of the multiple foreign exchange rates well. 
Yukihiro Aiba, Naomichi Hatano, Hideki Takayasu, Kouhei Marumo, Tokiko   Shimizu