Statistical Models for High Frequency Security Prices

Abstract

This article studies two extensions of the compound Poisson process with iid Gaussian innovations which are able to characterize important features of high frequency security prices. The first model explicitly accounts for the presence of the bid/ask spread encountered in price-driven markets. This model can be viewed as a mixture of the compound Poisson process model by Press and the bid/ask bounce model by Roll. The second model generalizes the compound Poisson process to allow for an arbitrary dependence structure in its innovations so as to account for more complicated types of market microstructure. Based on the characteristic function, we analyze the static and dynamic properties of the price process in detail. Comparison with actual high frequency data suggests that the proposed models are sufficiently flexible to capture a number of salient features of financial return data including a skewed and fat tailed marginal distribution, serial correlation at high frequency, time variation in market activity both at high and low frequency. The current framework also allows for a detailed investigation of the "market-microstructure-induced bias" in the realized variance measure and we find that, for realistic parameter values, this bias can be substantial. We analyze the impact of the sampling frequency on the bias and find that for non-constant trade intensity, "business" time sampling maximizes the bias but achieves the lowest overall MSE.

Keywords: compound poisson process, high frequency data, market microstructure, characteristic function, OU process, realized variance bias, optimal sampling