A New Model for Limit Order Book Dynamics*
This chapter proposes a model for limit order book dynamics. The model is formulated in a way that separates the modeling problem into a model for the level of the depth, and a model for the distribution of the depth, across specified bins. The decomposition combined with the use of a convenient Probit model allows the dynamics to be interpreted in a particularly simple way. Specifically, the level, average distance of the depth from the midquote, and the flatness or spread of the depth across the bins are modelled. The model for the level of the depth can be taken from off the shelf processes. The new part here is the model for the time-varying multinomial distribution. Simple low order models for the Probit are able to capture the strong temporal dependence in the shape of the distribution of the depth. Several economic variables are considered. Higher volatility predicts that the overall level of the depth will increase, but that depth moves away from the midquote and the distribution tends to flatten out, becoming more disperse.
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