Kybernetika 48 no. 1, 50-82, 2012

Probabilistic properties of the continuous double auction

Martin Šmíd

Abstract:

In this paper we formulate a general model of the continuous double auction. We (recursively) describe the distribution of the model. As a useful by-product, we give a (recursive) analytic description of the distribution of the process of the best quotes (bid and ask).

Keywords:

continuous double auction, limit order market, distribution

Classification:

91G80

References:

  1. D. J. Daley and D. Vere-Jones: An Introduction to the Theory of Point Processes. Second edition. Springer, New York 2003.   CrossRef
  2. J. Hoffmann-Jørgenson: Probability with a View Towards to Statistics I. Chapman and Hall, New York, 1994.   CrossRef
  3. O. Kallenberg: Foundations of Modern Probability. Second edition. Springer, New York 2002.   CrossRef
  4. H. Luckock: A steady-state model of the continuous double auction. Quantitative Finance 3 (2003), 385-404.   CrossRef
  5. S. Maslov: Simple model of a limit order driven market. Physica A 278 (2000), 571-578.   CrossRef
  6. S. Mike and J. D. Farmer: An empirical behavioral model of liquidity and volatility. J. Econom. Dynamics Control 32 (2008), 200-234.   CrossRef
  7. D. Pollard: A User's Guide to Measure Theoretic Probability. Cambridge Univ. Press, Cambridge 2002.   CrossRef
  8. M. Šmíd: On Approximation of Stochastic Programming Problems. PhD Thesis, Charles University, Department of Probability Statistics, 2004.   CrossRef
  9. M. Šmíd: Price tails in the Smith and Farmer's model. Bull. Czech Econometric Soc. 25 (2008), 31-40.   CrossRef
  10. M. Šmíd: Probabilistic Properties of the Continuous Double Auction. Research Report No. 2304. Institute of Information Theory and Automation, Prague 2011.   CrossRef
  11. E. Smith, J. D. Farmer, L. Gillemot and S. Krishnamurthy: Statistical theory of the continuous double auction. Quantitative Finance 3 (2003), 6, 481-514.   CrossRef