Efficient Estimation of Volatility Using High Frequency Data

22 Pages Posted: 16 Apr 2002

See all articles by Gilles O. Zumbach

Gilles O. Zumbach

University of Applied Sciences Western Switzerland - Geneva School of Business Administration

Fulvio Corsi

University of Pisa - Department of Economics; City University London

Adrian Trapletti

Independent

Date Written: February 21, 2002

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, seasonalities, and random arrival time of ticks. Moreover, we investigate the robustness of the estimators with respect to data frequency changes and gaps. Finally, we illustrate the behavior of the best estimators on empirical data.

Keywords: volatility estimators, high-frequency data, incoherent price formation, daily volatility

JEL Classification: C13, C15, C22

Suggested Citation

Zumbach, Gilles and Corsi, Fulvio and Trapletti, Adrian, Efficient Estimation of Volatility Using High Frequency Data (February 21, 2002). Available at SSRN: https://ssrn.com/abstract=306002 or http://dx.doi.org/10.2139/ssrn.306002

Gilles Zumbach (Contact Author)

University of Applied Sciences Western Switzerland - Geneva School of Business Administration ( email )

CH-1227 Geneva
Switzerland

Fulvio Corsi

University of Pisa - Department of Economics ( email )

via Ridolfi 10
I-56100 Pisa, PI 56100
Italy

HOME PAGE: http://people.unipi.it/fulvio_corsi/

City University London ( email )

Northampton Square
London, EC1V OHB
United Kingdom

Adrian Trapletti

Independent ( email )

Wildsbergstrasse 31
Uster CH-8610

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