Diffusive behavior and the modeling of characteristic times in limit order executions

Zoltán Eisler*, János Kertész, Fabrizio Lillo, Rosario N. Mantegna

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract (may include machine translation)

We present an empirical study of the first passage time (FPT) of order book prices needed to observe a prescribed price change, the time to fill (TTF) for executed limit orders and the time to cancel (TTC) for canceled orders in a double auction market. We find that the distribution of all three quantities decays asymptotically as a power law, but that of FPT has significantly fatter tails than that of TTF. Thus a simple first passage time model cannot account for the observed TTF of limit orders. We propose that the origin of this difference is the presence of cancelations. We outline a simple model that assumes that prices are characterized by the empirically observed distribution of the first passage time and orders are canceled randomly with lifetimes that are asymptotically power law distributed with an exponent LT. In spite of the simplifying assumptions of the model, the inclusion of cancelations is sufficient to account for the above observations and enables one to estimate characteristics of the cancelation strategies from empirical data.

Original languageEnglish
Pages (from-to)547-563
Number of pages17
JournalQuantitative Finance
Volume9
Issue number5
DOIs
StatePublished - Aug 2009
Externally publishedYes

Keywords

  • Censored data
  • Econophysics
  • First passage time
  • Limit order market
  • Microstructure
  • Time to fill

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