Berlin 2008 – wissenschaftliches Programm

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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 3: Financial Markets and Risk Management I

AKSOE 3.4: Vortrag

Montag, 25. Februar 2008, 11:45–12:15, EW 203

Characteristic times in limit order executions — •Zoltan Eisler^1,2, Janos Kertesz^1,3, Fabrizio Lillo^4,5, and Rosario N. Mantegna⁴ — ¹Science & Finance, Capital Fund Management, Paris, France — ²Department of Theoretical Physics, Budapest University of Technology and Economics, Budapest, Hungary — ³Laboratory of Computational Engineering, Helsinki University of Technology, Espoo, Finland — ⁴Dipartimento di Fisica e Tecnologie Relative, Universit‘a di Palermo, Palermo, Italy — ⁵Santa Fe Institute, Santa Fe, NM, USA

We present a study of the order book data of the London Stock Exchange. We study the first passage time of order book prices (i.e., the time needed to observe a prescribed price change), the time to fill (TTF) for executed limit orders and the time to cancel (TTC) for canceled ones. We find that the distribution of the first passage time decays asymptotically in time as a power law with an exponent λ_FPT = 1.5. The quantities TTF, and TTC are also asymptotically power law distributed with exponents λ_TTF = 1.8−2.2 and λ_FPT = 1.9−2.4, respectively. We outline a simple model, which assumes that prices are characterized by the empirically observed distribution of the first passage time and orders are canceled randomly. The model correctly predicts that λ_TTF≈ λ_TTC, and one can estimate from empirical data that the directly unobservable lifetimes are also power law distributed with an exponent λ_LT ≈ 1.6.