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      Second order approximations for limit order books

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          Abstract

          In this paper we derive a second order approximation for an infinite dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator (e.g. the volume standing at the top of the book). We study the fluctuations of the price and volume process relative to their first order approximation given in ODE-PDE form under two different scaling regimes. In the first case we suppose that price changes are really rare, yielding a constant first order approximation for the price. This leads to a measure valued SDE driven by an infinite dimensional Brownian motion in the second order approximation of the volume process. In the second case we use a slower rescaling rate, which leads to a non-degenerate first order approximation and gives a PDE with random coefficients in the second order approximation for the volume process.

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          Author and article information

          Journal
          24 August 2017
          Article
          1708.07394

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          60F17, 91G80
          q-fin.MF math.PR q-fin.TR

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