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

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 uni-versality 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 deposi-tion/cancellation rate is the critical parameter. Analytical results are fully supported by numerical simulations.