Foreign exchange market fluctuations as random walk in demarcated complex plane

Details Foreign exchange market fluctuations as random walk in demarcated complex plane Foreign exchange market fluctuations as random walk in demarcated complex plane

2003-08-15

arxiv.org/abs/physics/0308062v1

Physics

Computational Physics

Scientific paper

We show that time-dependent fluctuations $\{\Delta x\}$ in foreign exchange rates are accurately described by a random walk in a complex plane that is demarcated into the gain (+) and loss (-) sectors. $\{\Delta x\}$ is the outcome of $N$ random steps from the origin and $|\Delta x|$ is the square of the Euclidean distance of the final $N$-th step position. Sign of $\{\Delta x(t)\}$ is set by the $N$-th step location in the plane. The model explains not only the exponential statistics of the probability density of $\{\Delta x\}$ for G7 markets but also its observed asymmetry, and power-law dependent broadening with increasing time delay.

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