Power and Bipower Variation with Stochastic Volatility and Jumps

Posted: 29 Feb 2008

See all articles by Ole E. Barndorff-Nielsen

Ole E. Barndorff-Nielsen

University of Aarhus - Thiele Centre, Department of Mathematical Sciences

Neil Shephard

Harvard University

Multiple version iconThere are 2 versions of this paper

Date Written: 2004

Abstract

This article shows that realized power variation and its extension, realized bipower variation, which we introduce here, are somewhat robust to rare jumps. We demonstrate that in special cases, realized bipower variation estimates integrated variance in stochastic volatility models, thus providing a model-free and consistent alternative to realized variance. Its robustness property means that if we have a stochastic volatility plus infrequent jumps process, then the difference between realized variance and realized bipower variation estimates the quadratic variation of the jump component. This seems to be the first method that can separate quadratic variation into its continuous and jump components. Various extensions are given, together with proofs of special cases of these results. Detailed mathematical results are reported in Barndorff-Nielsen and Shephard (2003a).

Keywords: bipower variation, integrated variance, jump process, power variation, quadratic variation, realized variance, realized volatility, semimartingale, volatility

Suggested Citation

Barndorff-Nielsen, Ole E. and Shephard, Neil, Power and Bipower Variation with Stochastic Volatility and Jumps ( 2004). Journal of Financial Econometrics, Vol. 2, Issue 1, pp. 1-37, 2004. Available at SSRN: https://ssrn.com/abstract=821712

Ole E. Barndorff-Nielsen (Contact Author)

University of Aarhus - Thiele Centre, Department of Mathematical Sciences ( email )

Ny Munkegade
Aarhus, DK 8000
Denmark

Neil Shephard

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
1,642
PlumX Metrics