Dresden 2003 – wissenschaftliches Programm
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AKSOE: Physik sozio-ökonomischer Systeme
AKSOE 10: Finanzm
ärkte und Risikomanagement III
AKSOE 10.2: Vortrag
Donnerstag, 27. März 2003, 14:30–15:00, BAR/205
Exact Hurst exponent and crossover behavior in a limit order market model — •Richard Willmann1,2, 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.