Limit order book modelling -- a stochastic approach --

Abstract

We apply a stochastic model to study the continuous-time dynamics of a limit order book for AstraZeneca PLC. The model is analytically tractable and also captures core empirical properties of the order book, which permits us to compute various quantities of interest bypassing the use of simulation. Using the Laplace transform, we are able to compute the conditional distribution of di erent events given the state of the order book. In this thesis we compute probabilities of increase in the mid-price and probabilities of executing the bid before the midprice moves. Comparison with empirical frequencies shows that our model captures accurately the short-term dynamics of the limit order book. However, we noted the model is not always applicable due to inconsistencies in the proportionality of cancellation of some order book data.