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A Mathematical Approach to Order Book Modeling

  • Frederic Abergel
  • Aymen Jedidi
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    Motivated by the desire 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, we present a mathematical study of the order book as a multidimensional continuous-time Markov chain and derive several mathematical results in the case of independent Poissonian arrival times. In particular, we show that the cancellation structure is an important factor ensuring the existence of a stationary distribution and the exponential convergence towards it. We also prove, by means of the functional central limit theorem (FCLT), that the rescaled-centered price process converges to a Brownian motion. We illustrate the analysis with numerical simulation and comparison against market data.

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    File URL: http://arxiv.org/pdf/1010.5136
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    Paper provided by arXiv.org in its series Papers with number 1010.5136.

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    Date of creation: Oct 2010
    Date of revision: Mar 2013
    Handle: RePEc:arx:papers:1010.5136
    Contact details of provider: Web page: http://arxiv.org/

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