The statistical mechanics of currency exchange
It’s no secret that financial markets can be volatile. Stock prices change by the second. A currency can lose a third of its value in a matter of hours. To help make sense of those ups and downs, econophysicists take cues from statistical mechanical models of colloids, micron-sized particles immersed in fluid. Constantly jostled by the fluid molecules, colloids move along erratic trajectories known as random walks. Market prices—driven not by molecules but by profit-seeking traders—also seem to follow random walks. But whereas the statistics of a colloidal random walk can be unambiguously derived from the properties of the impinging molecules, researchers have struggled to establish a clear mathematical link between market-price fluctuations and trader behavior.
Misako Takayasu and her colleagues at the Tokyo Institute of Technology now think they’ve found such a link for at least one type of financial market: currency exchanges. The researchers examined a week’s worth of trades—specifically, purchases of US dollars with Japanese yen—at the online exchange market Electronic Broking Services. Of the millions of posted bids, only about 1% culminated in a transaction; prospective buyers and sellers frequently cancelled orders and adjusted their offers based on the latest sale price. From the trove of bids, cancellations, and transactions, the researchers identified a trend: When the value of the dollar changed from one transaction to the next by some small amount Δp, bidders tended to adjust their offer prices by an amount proportional to Δp. That so-called trend-following response saturates when Δp exceeds a certain threshold, around ¥0.01, or 1/100 of a cent. The resulting relationship between trader price adjustments and Δp can be approximated with a hyperbolic tangent curve.
Modelling a foreign exchange market as an ensemble of trend-following traders subject to statistical noise, Takayasu and company were able to quantitatively reproduce key market traits, including the mean spread—the difference between the price most buyers are willing to pay and the price most sellers are willing to accept—and probability distributions of Δp. The model suggests that although the currency exchange comprised more than a thousand participants, price fluctuations were driven mainly by a handful of high-frequency traders. (K. Kanazawa et al., Phys. Rev. Lett. 120, 138301, 2018 .)
