Model-based Measurement of Actual Volatility in High-Frequency Data

In this paper we aim to measure actual volatility within a model-based framework using high-frequency data. In the empirical finance literature it is known that tick-by-tick prices are subject to market micro-structure such as bid-ask bounces and trade information. Such market micro-structure effects become more and more apparent as prices or returns are sampled at smaller and smaller time intervals. High-frequency returns are used for the computation of realised volatility. Recent theoretical results have shown that realised volatility is a consistent estimator of actual volatility but when it is subject to micro-structure noise, the estimator diverges. Parametric and nonparametric methods can be adopted to account for the micro-structure bias. Here we measure actual volatility using a model that takes account of micro-structure noise together with intra-daily volatility patterns and stochastic volatility. The coefficients of this model are estimated by maximum likelihood methods that are based on importance sampling techniques. It is shown that such Monte Carlo techniques can be employed successfully for our purposes in a feasible way. As far as we know, this is a first serious attempt to model the basic components of the mean and variance of high-frequency prices simultaneously. An illustration is given for three months of tick-by-tick transaction prices of the IBM stock traded at the New York Stock Exchange.Importance sampling; Maximum likelihood estimation; Micro-structure noise; Realised variance; Stochastic volatility model