Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Estimation of volatility functionals: the case of a square root n window

Abstract : We consider a multidimensional Ito semimartingale regularly sampled on [0,t] at high frequency 1/\Delta_n, with \Delta_n going to zero. The goal of this paper is to provide an estimator for the integral over [0,t] of a given function of the volatility matrix, with the optimal rate 1/\sqrt{\Delta_n} and minimal asymptotic variance. To achieve this we use spot volatility estimators based on observations within time intervals of length k_n\Delta_n. In [5] this was done with k_n tending to infinity and k_n\sqrt{\Delta_n} tending to 0, and a central limit theorem was given after suitable de-biasing. Here we do the same with k_n of order 1/\sqrt{\Delta_n}. This results in a smaller bias, although more difficult to eliminate.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [6 references]  Display  Hide  Download
Contributor : Mathieu Rosenbaum <>
Submitted on : Monday, December 10, 2012 - 12:55:07 AM
Last modification on : Wednesday, December 9, 2020 - 3:14:46 PM
Long-term archiving on: : Monday, March 11, 2013 - 12:10:46 PM


Files produced by the author(s)


  • HAL Id : hal-00762969, version 1
  • ARXIV : 1212.1997


Jean Jacod, Mathieu Rosenbaum. Estimation of volatility functionals: the case of a square root n window. 2012. ⟨hal-00762969⟩



Record views


Files downloads