Intraday Transaction Price Dynamics

High frequency transaction prices exhibit two major characteristics: they are discrete in level and only exist at random transaction dates. In this paper, we seek to model transaction price dynamics, taking into account these two features. We specify the transaction price process as a Markov Chain with random transaction dates, and discuss various tools for dynamic analysis like the canonical decomposition, the scale and speed measures. The approach is applied to high frequency data on the stock Elf-Aquitaine traded on the Paris Bourse.