Financial Brownian particle in the layered order book fluid and Fluctuation-Dissipation relations

Yoshihiro Yura, Hideki Takayasu, Didier Sornette and Misako Takayasu

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Abstract: We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of a comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian particle and its surrounding fluid particles reflect specific layering interactions; in the inner-layer, the correlation is strong and with short memory while, in the outer-layer, it is weaker and with long memory. By interpreting and estimating the contribution from the outer-layer as a drag resistance, we demonstrate the validity of the fluctuation-dissipation relation (FDR) in this non-material Brownian motion process.

Date: 2014-01
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