Efficient Estimation of Volatility using High Frequency Data
Gilles Zumbach1 , Fulvio Corsi2, and Adrian Trapletti3
Olsen & Associates Research Institute for Applied Economics Seefeldstrasse 233, 8008 Z¨ rich, Switzerland. u phone: +41-1/386 48 48 Fax: +41-1/422 22 82

February 21, 2002 Keywords: volatility estimators, high-frequency data, incoherent price formation, daily volatility.

Abstract
The limitations of volatilities computed with daily data as well as simple statistical considerations strongly suggest to use intraday data in order to obtain accurate volatility estimates. Under a continuous time arbitrage-free setup, the quadratic variations of the prices would allow us, in principle, to construct an approximately error free estimate of volatility by using data at the highest frequency available. Yet, empirical data at very short time scales differ in many ways from the arbitrage-free continuous time price processes. For foreign exchange rates, the main difference originates in the incoherent structure of the price formation process. This market micro-structure effect introduces a noisy component in the price process leading to a strong overestimation of volatility when using naive estimators. Therefore, to be able to fully exploit the information contained in high frequency data, this incoherent effect needs to be discounted. In this contribution, we investigate several unbiased estimators that take into account the incoherent noise. One approach is to use a filter for pre-whitening the prices, and then using volatility estimators based on the filtered series. Another solution is to directly define a volatility estimator using tick-by-tick price differences, and including a correction term for the price formation effect. The properties of these estimators are investigated by Monte Carlo simulations. A number of important real-world effects are included in the simulated processes: realistic volatility and price dynamic, the incoherent effect,