This dissertation contributes to the research in the applied market micro-structure field, aiming to investigate the impact of a specific article of the MiFID II enforced on the 3rd of January 2018: the so-called tick size regime. It is constituted by three papers that see in the market regulators and policy-makers their optimal target. The first paper evaluates the consequences of the new regulation on UK minor venues in terms of liquidity and price discovery and highlights minor unintended consequences in the implementation of the new grid. The second paper builds on these conclusions and promotes an alternative to ESMA grid, a recalibration of the tick size that might lead to a greater orderliness of UK order books. Thethirdpaperendogenouslyinvestigatesthebehaviourofthemarketparticipants in the time frame around the MiFID II enforcement, simulating liquidity breakdowns thus providing the regulators with new simple metrics to detect and monitor abnormal market participants interactions.

We consider Sequential Monte Carlo Approximate Bayesian Computation (SMC ABC) as a method of calibration for the use of agent based models in market micro-structure. To date, there are no successful calibrations of agent based models to high frequency trading data. Here we test whether a more sophisticated calibration technique, SMC ABC, will achieve this feat on one of the leading agent based models in high frequency trading literature (the Preis-Golke-Paul-Schneider Agent Based Model (Preis et al., 2006)). We find that, although SMC ABC's naive approach of updating distributions can successfully calibrate simple toy models, such as autoregressive moving average models, it fails to calibrate this agent based model for high frequency trading. This may be for two key reasons, either the parameters of the model are not uniquely identifiable given the model output or the SMC ABC rejection mechanism results in information loss rendering parameters unidentifiable given insucient summary statistics.