In this thesis, we focus on two research problems in stock market microstructure. The first problem is to analyse institutional traders' intraday trading and their profitability. Using a unique data set from the exchange, we find that the institutional traders who can successfully predict intraday price movements in the first period are more likely to successfully predict price movements in the second period. In addition, institutional traders who can successfully predict intraday price movements for a certain time horizon and execute their trades in that horizon have on average 0.83 currency higher per trade profitability. Further, on average liquidity provision raises their per trade profitability by 4.27 currency.

The second problem is about limit order book modelling. We use a bivariate point process with stochastic intensities to model market buy and sell order arrivals. We derive recursive formulae for the projected intensities conditional on the observed history. And we propose a numerical scheme to compute the projected intensities. In the numerical example, we fit our model to a data set of market order arrivals using maximum likelihood estimation, and find that our model has smaller Akaike information criterion (AIC) and Bayesian information criterion (BIC) than the Hawkes model.