Ultra-High-Frequency Transaction Data Modeling and Application

This paper describes ultra-high-frequency data with marked point process, defines transaction process intensity to represent both transaction time interval changes and marks changes, derives sample function density and its maximum likelihood estimating formulation. As an example, when trade prices are Brown motions, price process and transaction arrival time process are independent each other, we have estimated stock price volatility. The results are that the less the sampling time interval, the nearer the estimated price volatility to that in ultra-high-frequency data.