On limit order book modelling

Abstract

This study analyzes a model of a limit order book developed by Cont and de Larrard in 2013. This model has attracted a lot of attention because of its analytical tractability and has been extended in various directions. Some errors in the results of Cont and de Larrard have been pointed out in the literature. In this work, we have undertaken a thorough analysis of this model to fill out the gaps in the proofs of the results and ascertain that the results are free of errors. It is very common, in a study involving randomness, to construct a simulation model that mimics the system under study and verify if the output of the simulation model matches the theoretical results obtained. We have constructed a simulation model for the limit order book considered by Cont and de Larrard and some of its extensions and ensured that the simulation outputs are in agreement with the theoretical results. Finally, we have considered another possible extension of Cont and de Larrard’s model using the fractional Gaussian noise in order to model dependence between the orders that arrive at the market.