IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v463y2016icp516-524.html
   My bibliography  Save this article

Limit order book and its modeling in terms of Gibbs Grand-Canonical Ensemble

Author

Listed:
  • Bicci, Alberto

Abstract

In the domain of so called Econophysics some attempts have been already made for applying the theory of thermodynamics and statistical mechanics to economics and financial markets. In this paper a similar approach is made from a different perspective, trying to model the limit order book and price formation process of a given stock by the Grand-Canonical Gibbs Ensemble for the bid and ask orders. The application of the Bose–Einstein statistics to this ensemble allows then to derive the distribution of the sell and buy orders as a function of price. As a consequence we can define in a meaningful way expressions for the temperatures of the ensembles of bid orders and of ask orders, which are a function of minimum bid, maximum ask and closure prices of the stock as well as of the exchanged volume of shares. It is demonstrated that the difference between the ask and bid orders temperatures can be related to the VAO (Volume Accumulation Oscillator), an indicator empirically defined in Technical Analysis of stock markets. Furthermore the derived distributions for aggregate bid and ask orders can be subject to well defined validations against real data, giving a falsifiable character to the model.

Suggested Citation

  • Bicci, Alberto, 2016. "Limit order book and its modeling in terms of Gibbs Grand-Canonical Ensemble," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 516-524.
  • Handle: RePEc:eee:phsmap:v:463:y:2016:i:c:p:516-524
    DOI: 10.1016/j.physa.2016.07.040
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711630471X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2016.07.040?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Szabolcs Mike & J. Doyne Farmer, 2005. "An empirical behavioral model of price formation," Papers physics/0509194, arXiv.org, revised Oct 2005.
    2. Ausloos, M., 2000. "Gas-kinetic theory and Boltzmann equation of share price within an equilibrium market hypothesis and ad hoc strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 385-392.
    3. Viaggiu, Stefano & Lionetto, Andrea & Bargigli, Leonardo & Longo, Michele, 2012. "Statistical ensembles for money and debt," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4839-4849.
    4. Smith, Eric & Foley, Duncan K., 2008. "Classical thermodynamics and economic general equilibrium theory," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 7-65, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alberto Bicci, 2016. "Limit Order Book and its modelling in terms of Gibbs Grand-Canonical Ensemble," Papers 1602.06968, arXiv.org, revised Feb 2016.
    2. Venkatasubramanian, Venkat & Luo, Yu & Sethuraman, Jay, 2015. "How much inequality in income is fair? A microeconomic game theoretic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 120-138.
    3. Roma, Antonio & Pirino, Davide, 2009. "The extraction of natural resources: The role of thermodynamic efficiency," Ecological Economics, Elsevier, vol. 68(10), pages 2594-2606, August.
    4. Arthur Matsuo Yamashita Rios de Sousa & Hideki Takayasu & Misako Takayasu, 2017. "Detection of statistical asymmetries in non-stationary sign time series: Analysis of foreign exchange data," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-18, May.
    5. Sylvain Barde, 2009. "The Google thought experiment: rationality, information and equilibrium in an exchange economy," SciencePo Working papers Main hal-01069373, HAL.
    6. Villas-Boas, Sofia B. & Judge, George, 2013. "An Information Theoretic Approach to Understanding the Micro Foundations of Macro Processes," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt82f7m32n, Department of Agricultural & Resource Economics, UC Berkeley.
    7. Willis, Geoff, 2011. "Why money trickles up – wealth & income distributions," MPRA Paper 30851, University Library of Munich, Germany.
    8. Glötzl, Erhard & Glötzl, Florentin & Richters, Oliver & Binter, Lucas, 2023. "General Constrained Dynamic Models in Economics - General Dynamic Theory of Economic Variables - Beyond Walras and Keynes," MPRA Paper 118314, University Library of Munich, Germany.
    9. Sergey Rashkovskiy, 2020. "Thermodynamics of markets," Papers 2010.10260, arXiv.org.
    10. Catalano, Michele & Di Guilmi, Corrado, 2019. "Uncertainty, rationality and complexity in a multi-sectoral dynamic model: The dynamic stochastic generalized aggregation approach," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 117-144.
    11. Leonardo Bargigli & Renato Giannetti, 2015. "The Italian Corporate System: SOEs, Private Firms and Institutions in a Network Perspective (1952-1983)," Working Papers - Economics wp2015_01.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    12. Rashkovskiy, S.A., 2021. "Economic thermodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    13. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2008. "Relation between bid-ask spread, impact and volatility in order-driven markets," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 41-57.
    14. Noe Rodriguez-Rodriguez & Octavio Miramontes, 2022. "Shannon entropy: an econophysical approach to cryptocurrency portfolios," Papers 2210.02633, arXiv.org.
    15. repec:spo:wpmain:info:hdl:2441/eu4vqp9ompqllr09hc01g3029 is not listed on IDEAS
    16. Chiarella Carl & Di Guilmi Corrado, 2015. "The limit distribution of evolving strategies in financial markets," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(2), pages 137-159, April.
    17. Noe Wiener, 2018. "Measuring Labor Market Segmentation from Incomplete Data," UMASS Amherst Economics Working Papers 2018-01, University of Massachusetts Amherst, Department of Economics.
    18. Leonardo Bargigli & Giovanni di Iasio & Luigi Infante & Fabrizio Lillo & Federico Pierobon, 2015. "Interbank markets and multiplex networks: centrality measures and statistical null models," Papers 1501.05751, arXiv.org.
    19. Winkler, Julian, 2023. "Managing fundamentals versus preferences: Re-balancing portfolios and stock returns," MPRA Paper 119149, University Library of Munich, Germany.
    20. Anirban Chakraborti & Dhruv Raina & Kiran Sharma, 2016. "Can an interdisciplinary field contribute to one of the parent disciplines from which it emerged?," Papers 1605.08354, arXiv.org.
    21. Marcel Ausloos & Herbert Dawid & Ugo Merlone, 2015. "Spatial Interactions in Agent-Based Modeling," Dynamic Modeling and Econometrics in Economics and Finance, in: Pasquale Commendatore & Saime Kayam & Ingrid Kubin (ed.), Complexity and Geographical Economics, edition 127, pages 353-377, Springer.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:463:y:2016:i:c:p:516-524. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.