We investigate high-frequency volatility models for analyzing intra-day tick by tick stock price changes using Bayesian estimation procedures. Our key interest is the extraction of intra-day volatility patterns from high-frequency integer price changes. We account for the discrete nature of the...

Stochastic processes arising in the description of the risk-neutral evolution of equity prices are reviewed. Starting with Brownian motion, I review extensions to Lévy and Sato processes. These processes have independent increments; the former are homogeneous in time, whereas the latter are...