Similarity and difference between colloidal random walk and financial random walk

Hideki Takayasu 

Sony Computer Science Laboratories (SONYCSL), 3-14-13 Higashigotanda Shinagawa, Tokyo 141-0022, Japan
Tokyo Institute of Technology, Yokohama 226-8502, Japan
Meiji University, 4-21-1 Nakano, Tokyo 164-8525, Japan


By analyzing high quality order-book data of Foreign Exchange Market, detail mechanism of random walk of market price has been clarified [1]. It is shown that both buy-side and sell-side of order-book have layered structures; the inner-layer which directly drive the motion of market price in short time scale, and the outer-layer which works oppositely as resistivity in long time scale. Langevin equation is naturally derived from the data for description of market price motion, demonstrating that the market price has effective inertial mass and surrounding orders show viscous resistivity,   quite similar to colloidal random walk in water molecules.

    Contrary to random walks in physical systems all quantities such as resistivity change in time and they can take different values for direction, up or down of the price motion. Extending this analogy we can define Knudsen number of market that quantitatively characterizes breakdown of continuum approximation [2]. It is shown that the value of Knudsen number is not small enough in general, and sometimes its value exceeds the threshold that requires discrete description even in the most fluidic market, EUR-USD.



[1] Yoshihiro Yura, Hideki Takayasu, Didier Sornette, Misako Takayasu

“Financial Brownian Particle in the Layered Order-Book Fluid and Fluctuation -Dissipation Relations” , Phys. Rev. Lett. 112, 098703, 5 pages (2014, OPEN ACCESS)

[2] Yoshihiro Yura, Hideki Takayasu, Didier Sornette, Misako Takayasu

“Financial Knudsen number: breakdown of continuous price dynamics and asymmetric buy and sell structures confirmed by high precision order book information”, Phys. Rev. E to appear.


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Presentation: Invited oral at 8 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych", by Hideki Takayasu
See On-line Journal of 8 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych"

Submitted: 2015-08-28 15:17
Revised:   2015-11-07 14:53