Forecasting Volatility Using Tick by Tick Data

Abstract

The paper builds an econometric model for estimating the volatility of unobserved efficient price change using tick by tick data. We model the joint density of the marked point process of duration and tick by tick returns within an ACD-GARCH framework. We first model the duration variable as an ACD process that could potentially depend on past returns. We then model the return variable conditioning on its current duration as well as past information. The observed return process admits a state space model, where the unobserved efficient price innovation and microstructure noises serve as state variables. After adjusting for bid-ask spread and a non-linear function of durations, tick by tick returns are distributed independently of durations, with volatility that admits a GARCH process. We apply the above model to frequently traded NYSE stock transactions data. It appears that contemporaneous duration has little affect on the conditional volatility per trade, which means per second volatility is inversely related to the duration between trades. This is consistent with the result of Engle (2000) and Easley and O'Hara (1987). The model is used to obtain a new, model-based estimate of daily, realized volatility as well as the volatility of efficient price changes.Volatility is forecasted over calendar time intervals by simulation. The distribution of the number of trades is central in forming these forecasts.

Keywords: volatility, tick by tick data, duration, microstructure noise, ACD, Kalman Filter