Advanced Search
MyIDEAS: Login

A Mathematical Approach to Order Book Modelling

Contents:

Author Info

  • Frédéric Abergel

    ()
    (MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris, FiQuant - Chaire de finance quantitative - Ecole Centrale Paris)

  • Aymen Jedidi

    ()
    (MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris, FiQuant - Chaire de finance quantitative - Ecole Centrale Paris)

Registered author(s):

    Abstract

    We present a mathematical study of the order book as a multidimensional continuous- time Markov chain where the order flow is modeled by independent Poisson processes. Our aim is to bridge the gap between the microscopic description of price formation (agent- based modeling), and the Stochastic Differential Equations approach used classically to describe price evolution at macroscopic time scales. To do this, we rely on the theory of infinitesimal generators and Foster-Lyapunov stability criteria for Markov chains. We motivate our approach using an elementary example where the spread is kept constant ("perfect market making"). Then we compute the infinitesimal generator associated with the order book in a general setting, and link the price dynamics to the instantaneous state of the order book. In the last section, we prove that the order book is ergodic - in particular it has a stationary distribution - that it converges to its stationary state exponentially fast, and that the large-scale limit of the price process is a Brownian motion.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://hal.archives-ouvertes.fr/docs/00/82/18/58/PDF/main_hal.pdf
    Download Restriction: no

    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00621253.

    as in new window
    Length:
    Date of creation: 2013
    Date of revision:
    Handle: RePEc:hal:wpaper:hal-00621253

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00621253
    Contact details of provider:
    Web page: http://hal.archives-ouvertes.fr/

    Related research

    Keywords:

    This paper has been announced in the following NEP Reports:

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
    2. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-00621253. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.