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...

Intraday high-frequency data of stock returns exhibit not only typical characteristics (e.g., volatility clustering and the leverage effect) but also a cyclical pattern of return volatility that is known as intraday seasonality. In this paper, we extend the stochastic volatility (SV) model for...

We estimate a general microstructure model of the transitory and permanent impact of order flow on stock prices. Jumps are detected in both the transaction price (observation equation) and fundamental value (state equation). The model's parameters and variances are updated in real time. Prices...

This paper studies the information content of the S&P 500 and VIX markets on the volatility of the S&P 500 returns. We estimate a flexible affine model based on a joint time series of underlying indexes and option prices on both markets. An extensive model specification analysis reveals that...