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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 10: Finanzm
ärkte und Risikomanagement III

AKSOE 10.2: Talk

Thursday, March 27, 2003, 14:30–15:00, BAR/205

Exact Hurst exponent and crossover behavior in a limit order market model — •Richard Willmann^1,2, Gunter M. Schütz¹, and Damien Challet³ — ¹Forschungszentrum Jülich, Germany — ²Weizmann Institute of Science, Israel — ³Oxford University, UK

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.