Exact Hurst exponent and crossover behavior in a limit order market model

Details Exact Hurst exponent and crossover behavior in a limit order market model Exact Hurst exponent and crossover behavior in a limit order market model

2002-06-24

arxiv.org/abs/cond-mat/0206446v1

Physica A 316, 430 (2002)

Physics

Condensed Matter

Statistical Mechanics

13 pages, 10 figures, accepted for publication in Physica A

Scientific paper

10.1016/S0378-4371(02)01217-7

An exclusion particle model is considered as a highly simplified model of a limit order market. Its price behavior reproduces the well known crossover from over-diffusion (Hurst exponent H>1/2) to diffusion (H=1/2) when the time horizon is increased, provided that orders are allowed to be canceled. For early times a mapping to the totally asymmetric exclusion process yields the exact result H=2/3 which is in good agreement with empirical data. The underlying universality class of the exclusion process suggests some robustness of the exponent with respect to changes in the trading rules. In the crossover regime the Hurst plot has a scaling property where the bulk deposition/cancellation rate is the critical parameter. Analytical results are fully supported by numerical simulations.

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