Efficient estimation of integrated volatility in presence of infinite variation jumps with multiple activity indices

Jean Jacod*, Viktor Todorov

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Scopus citations

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 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 β1 > … ≥ βM ≥ 1.

Original languageEnglish (US)
Title of host publicationThe Fascination of Probability, Statistics and their Applications
Subtitle of host publicationIn Honour of Ole E. Barndorff-Nielsen
PublisherSpringer International Publishing
Pages317-341
Number of pages25
ISBN (Electronic)9783319258263
ISBN (Print)9783319258249
DOIs
StatePublished - Jan 1 2015

Keywords

  • Central limit theorem
  • Integrated volatility
  • Itô semimartingale
  • Jump activity
  • Jumps
  • Quadratic variation
  • Stable process

ASJC Scopus subject areas

  • Mathematics(all)

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