Paul Krühner: On the Brownian limit order book dynamics

In this talk we introduce a simplistic, yet non-trivial, model for the (LOB) limit order book in discrete time and space. The underlying dynamics are motivated by the Cox-Ross-Rubinstein (CRR) model and as such it is hoped that our model could be used as a benchmark LOB model. Similar to the known fact that a scaled CRR model converges to the Black-Scholes (BS) model, the driving noise of our model converges on large scale to a BS model as well and the LOB is generated by its behaviour. Furthermore, we identify the stochastic behaviour of the LOB as good as possible, analyse the length of trading clusters and derive a convenient view on the timing of order execution.