A modelling framework for the prices and times of trades made on the New York stock exchange

In this chapter we propose using compound Poisson processes to model trade-by-trade financial data. Our main focus will be on developing specific types of Cox processes in order to accurately depict the trading process. We study the problem of signal extracting the intensity of the trading process. We finish by studying the implication for price changes over pre-specified intervals of times, such as 30 seconds, 20 minutes or a day and assessing the empirical plausibility of OU based models for the intensity of the trading process.