Realized Wavelet-Based Estimation of Integrated Variance and Jumps in the Presence of Noise

Quantitative Finance (2015) Vol. 15, No. 8, 1347-1364

28 Pages Posted: 8 Apr 2012 Last revised: 15 Oct 2017

See all articles by Jozef Baruník

Jozef Baruník

Charles University in Prague - Department of Economics; Institute of Information Theory and Automation, Prague

Lukas Vacha

Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic; Charles University in Prague - Department of Economics

Date Written: February 10, 2012

Abstract

We introduce wavelet-based methodology for estimation of realized variance allowing its measurement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the realized variance into several investment horizons and jumps. Basing our estimator in the two-scale realized variance framework, we are able to utilize all available data and get feasible estimator in the presence of microstructure noise as well. The estimator is tested in a large numerical study of the finite sample performance and is compared to other popular realized variation estimators. We use different simulation settings with changing noise as well as jump level in different price processes including long memory fractional stochastic volatility model. The results reveal that our wavelet-based estimator is able to estimate and forecast the realized measures with the greatest precision. Our time-frequency estimators not only produce feasible estimates, but also decompose the realized variation into arbitrarily chosen investment horizons. We apply it to study the volatility of forex futures during the recent crisis at several investment horizons and obtain the results which provide us with better understanding of the volatility dynamics.

Keywords: quadratic variation, realized variance, jumps, market microstructure noise, wavelets

JEL Classification: C14, C53, G17

Suggested Citation

Barunik, Jozef and Vacha, Lukas, Realized Wavelet-Based Estimation of Integrated Variance and Jumps in the Presence of Noise (February 10, 2012). Quantitative Finance (2015) Vol. 15, No. 8, 1347-1364. Available at SSRN: https://ssrn.com/abstract=2035395 or http://dx.doi.org/10.2139/ssrn.2035395

Jozef Barunik (Contact Author)

Charles University in Prague - Department of Economics ( email )

Opletalova 26
Prague 1, 110 00
Czech Republic

HOME PAGE: http://ies.fsv.cuni.cz/en/staff/barunik

Institute of Information Theory and Automation, Prague ( email )

Pod vodarenskou vezi 4
CZ-18208 Praha 8
Czech Republic

HOME PAGE: http://staff.utia.cas.cz/barunik/home.htm

Lukas Vacha

Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic ( email )

Pod vodarenskou vezi 4
Praha, CZ-18208
Czech Republic

Charles University in Prague - Department of Economics ( email )

Opletalova 26
Prague, 11000
Czech Republic

Register to save articles to
your library

Register

Paper statistics

Downloads
82
Abstract Views
715
rank
300,623
PlumX Metrics