Regensburg 2013 – wissenschaftliches Programm

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 3: Financial Markets and Risk Management II

SOE 3.3: Vortrag

Montag, 11. März 2013, 11:15–11:30, H37

Triangular arbitrages in foreign exchange markets — •Kenta Yamada¹, Takatoshi Ito², Hideki Takayasu³, and Misako Takayasu⁴ — ¹Waseda University, Tokyo, Japan — ²University of Tokyo, Tokyo, Japan — ³Sony CSL, Tokyo, Japan — ⁴Tokyo Institute of Technology, Tokyo, Japan

We confirm triangular arbitrages exist in foreign exchange markets by using high frequency data for 12 years from 1999 to 2010. When we make a triangular exchange such as yen to dollar, dollar to euro and then euro back to yen, usually we lose money because of the spread which is the difference between the bid price and the offer price. However sometimes we have a chance to make a profit. This arbitrage opportunity is against non-arbitrage principles in economics. These triangular arbitrage opportunities were originally identified by Aiba et. al. in 2002 [1]. They realized the triangular arbitrage opportunity existed by analyzing the foreign exchange market data for two months in 1999, and they found these triangular opportunities exist about 6.4 percent of the time. In our study we observed a consistent value in the same period, while the probability of arbitrage on January 2010 was only 0.1 percent. We calculated the number of triangular arbitrage opportunities and the disappearance probability of triangular arbitrages within one second each month for 12 years, and modeled the occurrence of the triangular arbitrage with volatility, the number of deals and the number of AI traders [2].

[1] Yukihiro Aiba, et. al., Physica A 310 (2002) 467-479.

[2] Takatoshi Ito, et. al. , NBER Working Paper No. 18541 (2012).