How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?

Almut Veraart

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: This paper studies the impact of jumps on volatility estimation and inference based on various realised variation measures such as realised variance, realised multipower variation and truncated realised multipower variation. We review the asymptotic theory of those realised variation measures and present a new estimator for the asymptotic ‘variance’ of the centered realised variance in the presence of jumps. Next, we compare the finite sample performance of the various estimators by means of detailed Monte Carlo studies where we study the impact of the jump activity, the jump size of the jumps in the price and the presence of additional independent or dependent jumps in the volatility on the finite sample performance of the various estimators. We find that the finite sample performance of realised variance, and in particular of the log–transformed realised variance, is generally good, whereas the jump–robust statistics turn out not to be as jump robust as the asymptotic theory would suggest in the presence of a highly active jump process. In an empirical study on high frequency data from the Standard & Poor’s Depository Receipt (SPY), we investigate the impact of jumps on inference on volatility by realised variance in practice.

Keywords: Realised variance; realised multipower variation; truncated realised variance; inference; stochastic volatility; jumps; priceLength: 48 (search for similar items in EconPapers)
JEL-codes: C10 C14 C58 G10 (search for similar items in EconPapers)
Date: 2010-09-18
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-mst
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Journal Article: How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps? (2011)
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