Efficient Estimation of Integrated Volatility in Presence of Infinite Variation Jumps with Multiple Activity Indices

Jean Jacod () and Viktor Todorov ()
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Jean Jacod: Université Pierre et Marie Curie–P6, Institut de Mathématiques de Jussieu, CNRS – UMR 7586
Viktor Todorov: Northwestern University, Department of Finance

A chapter in The Fascination of Probability, Statistics and their Applications, 2016, pp 317-341 from Springer

Abstract: Abstract In a recent paper [6], we derived a rate efficient (and in some cases variance efficient) estimator for the integrated volatility of the diffusion coefficient of a process in presence of infinite variation jumps. The estimation is based on discrete observations of the process on a fixed time interval with asymptotically shrinking equidistant observation grid. The result in [6] is derived under the assumption that the jump part of the discretely-observed process has a finite variation component plus a stochastic integral with respect to a stable-like Lévy process with index $$\beta >1$$ β > 1 . Here we show that the procedure of [6] can be extended to accommodate the case when the jumps are a mixture of finitely many integrals with respect to stable-like Lévy processes with indices $$\beta _1>\cdots >\beta _M\ge 1$$ β 1 > ⋯ > β M ≥ 1 .

Keywords: Central limit theorem; Integrated volatility; Itô semimartingale; Jumps; Jump activity; Quadratic variation; Stable process; 60F05; 60F17; 60G51; 60G07 (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-25826-3_15

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DOI: 10.1007/978-3-319-25826-3_15

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