Bernoulli

  • Bernoulli
  • Volume 13, Number 3 (2007), 601-622.

Are volatility estimators robust with respect to modeling assumptions?

Yingying Li and Per A. Mykland

Full-text: Open access

Abstract

We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel Q. Special cases include additive error, rounding and combinations thereof. Our main result is that, subject to smoothness conditions, the two scales realized volatility is robust to the form of contamination Q. To push the limits of our result, we show what happens for some models that involve rounding (which is not, of course, smooth) and see in this situation how the robustness deteriorates with decreasing smoothness. Our conclusion is that under reasonable smoothness, one does not need to consider too closely how the microstructure is formed, while if severe non-smoothness is suspected, one needs to pay attention to the precise structure and also the use to which the estimator of volatility will be put.

Article information

Source
Bernoulli, Volume 13, Number 3 (2007), 601-622.

Dates
First available in Project Euclid: 7 August 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1186503478

Digital Object Identifier
doi:10.3150/07-BEJ6067

Mathematical Reviews number (MathSciNet)
MR2348742

Zentralblatt MATH identifier
1129.62097

Keywords
bias correction local time market microstructure martingale measurement error realized volatility robustness subsampling two scales realized volatility (TSRV)

Citation

Li, Yingying; Mykland, Per A. Are volatility estimators robust with respect to modeling assumptions?. Bernoulli 13 (2007), no. 3, 601--622. doi:10.3150/07-BEJ6067. https://projecteuclid.org/euclid.bj/1186503478


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