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

Tinbergen Institute Discussion Paper No. 2005-002/4

26 Pages Posted: 10 Jan 2005

See all articles by Borus Jungbacker

Borus Jungbacker

VU University Amsterdam - Department of Economics

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics; Tinbergen Institute; Aarhus University - CREATES

Date Written: January 2005

Abstract

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.

Keywords: Importance sampling, Maximum likelihood estimation, Micro-structure noise, Realised variance, Stochastic volatility model

JEL Classification: C22, C53, G15

Suggested Citation

Jungbacker, Borus and Koopman, Siem Jan, Model-Based Measurement of Actual Volatility in High-Frequency Data (January 2005). Tinbergen Institute Discussion Paper No. 2005-002/4, Available at SSRN: https://ssrn.com/abstract=645782 or http://dx.doi.org/10.2139/ssrn.645782

Borus Jungbacker (Contact Author)

VU University Amsterdam - Department of Economics ( email )

De Boelelaan 1105
1081 HV Amsterdam
Netherlands

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31205986019 (Phone)

HOME PAGE: http://sjkoopman.net

Tinbergen Institute ( email )

Gustav Mahlerplein 117
1082 MS Amsterdam
Netherlands

HOME PAGE: http://personal.vu.nl/s.j.koopman

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

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