Abstract
In the present work we introduce a novel multi-agent model with the aim to reproduce the dynamics of a double auction market at microscopic time scale through a faithful simulation of the matching mechanics in the limit order book. The agents follow a noise decision making process where their actions are related to a stochastic variable, the market sentiment, which we define as a mixture of public and private information. The model, despite making just few basic assumptions over the trading strategies of the agents, is able to reproduce several empirical features of the high-frequency dynamics of the market microstructure not only related to the price movements but also to the deposition of the orders in the book.
Similar content being viewed by others
References
M. Bartolozzi, C. Mellen, F. Chan, Internal report, Boronia Capital, 2007a
J.-P. Bouchaud, M. Potters, Theory of financial risk (Cambridge University Press, Cambridge, 1999)
R.N. Mantegna, H.E. Stanley, An introduction to econophysics: correlation and complexity in finance (Cambridge University Press, Cambridge, 1999)
W. Paul, J. Baschnagel, Stochastic Process from Physics to Finance (Springer, Berlin, 1999)
J. Voit, The Statistical Mechanics of Financial Markets (Spriger-Verlag, Berlin, 2005)
R.E. Bailey, The economics of financial markets (Cambridge University Press, Cambridge, UK, 2005)
P. Bak, M. Paczuski, M. Shubik, Physica A 246, 430 (1997)
S. Maslov, Physica A 278, 571 (2000)
L. Matassini, F. Franci, How traders enter the market through the book (2001), preprint arXiv:cond-mat/0103106
M. Raberto, S. Cinotti, S.M. Focardi, M. Marchesi, Physica A 299, 319 (2001)
E. Smith, J.D. Farmer, L. Gillemot, S. Krishnamurthy, Quant. Financ. 3, 481 (2003)
M.G. Daniels, J.D. Farmer, L. Gillemot, G. Iori, Smith, E. Phys. Rev. Lett. 90, 1008102 (2003)
G. Iori, M.G. Daniels, J.D. Farmer, L. Gillemo, S. Krishnamurthy, E. Smith, Physica A 324, 146 (2003)
J.D. Farmer, P. Patelli, I.I. Zovko, Proc. Natl. Acad. Sci. USA 102, 2254 (2005)
S. Mike, J.D. Farmer, J. Econ. Dyn. Control 32, 2000 (2008)
A. Zaccaria, M. Cristelli, V. Alfi, F. Ciulla, L. Pietronero, Phys. Rev. E 81, 066101 (2010)
F. Slanina, Critical comparison of several order-book models for stock market fluctuations (2008), preprint arXiv: physics/0801.0631
M. O'Hara, Market Microstructure Theory (Blackwell Publishing, Malden, USA, 1997)
G. Fusai, A. Ronconi, Implementing models in quantitative finance: methods and cases (Springer-Verlag, Berlin, 2008)
D. Cutler, J. Poterba, L. Summers, Journal of Portfolio Managment 15, 4 (1989)
A. Joulin, A. Lefevre, D. Grunberg, J.-P. Bouchaud, Stock price jumps: news and volume play a minor role, Wilmott Magazine Sep/Oct, 1–7 (2008)
R. Cont, J.-P. Bouchaud, Macroeconomics Dynamics 4, 170 (2000)
M. Bartolozzi, A.W. Thomas, Phys. Rev. E 69, 046112 (2004)
J.-P. Bouchaud, M. Mézard, M. Potters, Quant. Financ. 2, 251 (2002)
C.-K. Peng, S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley, A.L. Goldberger, Phys. Rev. E 49, 1685 (1994)
M. Bartolozzi, C. Mellen, T. Di Matteo, T. Aste, Eur. Phys. J. B 58, 207 (2007b)
H. Hurst, Trans. Amer. Soc. Civil Eng. 116, 770 (1951)
J. Feder, Fractals (Plenum Press, New York & London, 1988)
B. Efron, R. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall, London, 1994)
J. Liu, P. Cizeau, M. Meyer, C.-K. Peng, H. Stanley, Physica A 245, 437 (1997)
P. Gopikrishnan, V. Plerou, L. Amaral, M. Meyer, H.-E. Stanley, Phys. Rev. E 60, 5305 (1999)
Y. Liu, P. Gopikrishnan, P. Cizeau, M. Meyer, C.-K. Peng, H. Stanley, Phys. Rev. E 60, 1390 (1999)
X. Gabaix, P. Gopikrishnan, V. Pleru, H.E. Stanley, Nature 423, 267 (2003)
J.D. Farmer, L. Gillemot, F. Lillo, S. Mike, A. Sen, Quant. Financ. 4, 383 (2004)
F. Lillo, M.J.D. Farmer, Fluc. Noise lett. 5, L209 (2005)
P. Weber, B. Rosenow, Quant. Financ. 5, 357 (2005)
J.D. Farmer, Quant. Financ. 6, 1 (2006)
P. Weber, B. Rosenow, Quant. Financ. 6, 7 (2006)
F. Lillo, M.J.D. Farmer, Nonlinear Dynamics and Econometrics 8, 1 (2004)
V. Plerou, P. Gopikrishnan, H.-E. Stanley, Phys. Rev. E 71, 046131 (2005)
D. Cajueiro, B. Tabak, Physica A 373, 627 (2007)
G.-F. Gu, W. Chen, W.-X. Zhou, Eur. Phys. J. B 57, 81 (2007)
D. Sornette, Why stock market crash (Princeton University Press, Princeton and Oxford, 2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bartolozzi, M. A multi agent model for the limit order book dynamics. Eur. Phys. J. B 78, 265–273 (2010). https://doi.org/10.1140/epjb/e2010-10406-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2010-10406-4