Tokiko Shimizu

Predictability of currency market exchange

We analyze tick data of yen–dollar exchange with a focus on its up and down movement. We show that there exists a rather particular conditional probability structure with such high frequency data. This result provides us with evidence to question one of the basic assumptions of the traditional market theory, where such bias in high frequency price movements is regarded as not present. We also construct systematically a random walk model reflecting this probability structure.

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.

A characteristic time scale in dollar–yen exchange rates

Here we analyze tick data of yen–dollar exchange using random walk methods. We find that there exists a characteristic time scale approximately at 10 min. According to the results at time scales shorter than 10 min, the market exhibits anti-persistence meaning that it self-organizes so as to restore a given tendency. For time scales longer than 10 min the market approaches a behavior appropriate to pure Brownian motion.

A dynamical structure of high frequency currency exchange market

We analyze tick-by-tick data, the most high frequency data available, of yen–dollar currency exchange rates. We show that a dynamical structure can be observed in binarized data indicating the direction of up and down movement of prices, which is not apparently seen from the price change itself. This result is consistent with our previous study that there exists a conditional probabilistic structure in binarized data. The dynamical and probabilistic structure which we found could indicate that dealers’ decision making is based on a binary strategy, even if they are unconscious of this fact.

Triangular arbitrage and negative auto-correlation of foreign exchange rates

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.