University of Chicago
NBER Working Papers and Publications
|October 2005||Edgeworth Expansions for Realized Volatility and Related Estimators|
with Per A. Mykland, Yacine Ait-Sahalia: t0319
This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we compute Edgeworth expansions for such estimators. Unlike the usual expansions, we have found that in order to obtain meaningful terms, one needs to let the size of the noise to go zero asymptotically. The results have application to Cornish-Fisher inversion and bootstrapping.
|May 2005||Ultra High Frequency Volatility Estimation with Dependent Microstructure Noise|
with Yacine Ait-Sahalia, Per A. Mykland: w11380
We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for that purpose will work even when the noise exhibits time series dependence, analyze in that context a refinement of this approach based on multiple time scales, and compare empirically our different estimators to the standard realized volatility.
Published: Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January. citation courtesy of
|November 2003||A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data|
with Per A. Mykland, Yacine Ait-Sahalia: w10111
It is a common practice in finance to estimate volatility from the sum of frequently-sampled squared returns. However market microstructure poses challenges to this estimation approach, as evidenced by recent empirical studies in finance. This work attempts to lay out theoretical grounds that reconcile continuous-time modeling and discrete-time samples. We propose an estimation approach that takes advantage of the rich sources in tick-by-tick data while preserving the continuous-time assumption on the underlying returns. Under our framework, it becomes clear why and where the usual' volatility estimator fails when the returns are sampled at the highest frequency.
Published: Zhang, Lan, Per A. Mykland and Yacine Ait-Sahalia. "A Tale Of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, 2005, v100(472,Dec), 1394-1411. citation courtesy of