Estimating Stochastic Volatility and Jumps Using High-Frequency Data and Bayesian Methods

25 Pages Posted: 20 Jan 2015

See all articles by Milan Fičura

Milan Fičura

University of Economics, Prague - Faculty of Finance and Accounting

Jiri Witzany

University of Economics in Prague

Date Written: January 19, 2015

Abstract

We are comparing two approaches for stochastic volatility and jumps estimation in the EUR/USD time series - the non-parametric power-variation approach using high-frequency returns, and the parametric Bayesian approach (MCMC estimation of SVJD models) using daily returns. We find that both of the methods do identify continuous stochastic volatility similarly, but they do not identify similarly the jump component. Firstly - the jumps estimated using the non-parametric high-frequency estimators are much more numerous than in the case of the Bayesian method using daily data. More importantly - we find that the probabilities of jump occurrences assigned to every day by both of the methods are virtually no rank-correlated (Spearman rank correlation is 0.0148) meaning that the two methods do not identify jumps at the same days. Actually the jump probabilities inferred using the non-parametric approach are not much correlated even with the daily realized variance and the daily squared returns, indicating that the discontinuous price changes (jumps) observed on high-frequencies may not be distinguishable (from the continuous volatility) on the daily frequency. As an additional result we find strong evidence for jump size dependence and jump clustering (based on the self-exciting Hawkes process) of the jumps identified using the non-parametric method (the shrinkage estimator).

Keywords: Stochastic volatility, Bayesian inference, MCMC, Realized variance, Bipower variation, Shrinkage estimator, Jump clustering, Self-Exciting jumps, Hawkes process

JEL Classification: C11, C14, C15, C22, G1

Suggested Citation

Fičura, Milan and Witzany, Jiri, Estimating Stochastic Volatility and Jumps Using High-Frequency Data and Bayesian Methods (January 19, 2015). Available at SSRN: https://ssrn.com/abstract=2551807 or http://dx.doi.org/10.2139/ssrn.2551807

Milan Fičura

University of Economics, Prague - Faculty of Finance and Accounting ( email )

VŠE v Praze
Nám. W. Churchilla 4
130 67
Czech Republic

Jiri Witzany (Contact Author)

University of Economics in Prague ( email )

Winston Churchilla Sq. 4
Prague 3, 130 67
Czech Republic

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