Efficient estimation of integrated volatility in presence of infinite variation jumps

Jean Jacod, Viktor Todorov

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

We propose new nonparametric estimators of the integrated volatility of an Itô semimartingale observed at discrete times on a fixed time interval with mesh of the observation grid shrinking to zero. The proposed estimators achieve the optimal rate and variance of estimating integrated volatility even in the presence of infinite variation jumps when the latter are stochastic integrals with respect to locally "stable" Lévy processes, that is, processes whose Lévy measure around zero behaves like that of a stable process. On a first step, we estimate locally volatility from the empirical characteristic function of the increments of the process over blocks of shrinking length and then we sum these estimates to form initial estimators of the integrated volatility. The estimators contain bias when jumps of infinite variation are present, and on a second step we estimate and remove this bias by using integrated volatility estimators formed from the empirical characteristic function of the high-frequency increments for different values of its argument. The second step debiased estimators achieve efficiency and we derive a feasible central limit theorem for them.

Original languageEnglish (US)
Pages (from-to)1029-1069
Number of pages41
JournalAnnals of Statistics
Volume42
Issue number3
DOIs
StatePublished - Jun 2014

Keywords

  • Central limit theorem
  • Integrated volatility
  • Itô semimartingale
  • Quadratic variation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Efficient estimation of integrated volatility in presence of infinite variation jumps'. Together they form a unique fingerprint.

Cite this