A Theoretical Model of the Limit Order Book and Some Applications

Random measures are used to describe the evolution of the limit order book. A new model for limit order arrival is proposed which enables us to construct a model of the order book. Our model is flexible enough to be fitted to empirical observations. It turns out that the limit order book will be a mixed Poisson process at every point in time. We describe the behaviour of the order book in the long run. Some applications to the optimal liquidation of a large position of stock holdings are given. A limit order strategy and a market order strategy are compared and conditions are given as to which one should be given priority. Finally, we show that naturally a new type of options occurs, a reverse Asian fixed strike lookback option.