Abstract: 
High frequency financial data has become an essential component of the digital world, giving rise to an increasing number of estimators. However, it is hard to reliably assess the uncertainty of such estimators. The Observed Asymptotic Variance (observed AVAR) is a non-parametric (squared) standard error for high-frequency-based estimators. We have earlier developed such an AVAR with time-discretization and two tuning parameters (per dimension). We here propose a better estimator C-AVAR by passing to continuous time. This is natural since observations are typically irregularly spaced. The C-AVAR only depends on a single tuning parameter δ, which permits a deeper analysis. We provide an expansion which shows that, when estimating the AVAR, there is a tradeoff (over a large range of δ) between edge effect and the volatility of the spot parameter. The edge effect is given with exact order.

The continuous-δ formulation is also useful in that it permits averaging across δ. This averaging is helpful (in data) because it smooths out edge effects. The averaging, as well as the continuous-time formulation, also means that the new estimator is more correct from a
sufficiency standpoint.

We show in a data illustration that the C-AVAR provides reasonable values for standard error when estimating integrated volatility in the presence of microstructure noise. As a by-product, the C-AVAR provides an interesting estimator of the volatility of volatility (or other spot process). As we shall also see in our data illustration, the estimator is able to pick out important dates in recent financial history.

Based on joint work with Per A. Mykland.

 

Bio:
Lan Zhang is Professor of Finance at the University of Illinois Chicago. Her research focuses on big data in finance and high frequency financial econometrics. Lan Zhang has developed a number of inferential methods for high dimensional and high frequency financial data, including the two-scale and multi-scale realized volatility estimators (TSRV, MSRV) under market microstructure, as well as high frequency PCA.

Professor Zhang is an elected Fellow at the Society for Financial Econometrics (2016) and at the Institute of Mathematical Statistics (2022). Zhang has published widely in leading journals including Econometrica, Review of Financial Studies, Journal of Econometrics, Journal of the American Statistical Association, Bernoulli, and Annals of Statistics. She is the co-editor for the Special Issue on "Big Data in Predictive Dynamic Econometric Modeling", Journal of Econometrics.  Her work on the interface between statistics and finance has received grants from the National Science Foundation (2002-2005, 2014-2017, 2017-2020, 2020-2024), National Institute of Health (2003-2006), and Morgan Stanley Research Fund on Market Microstructure (2004-2005). 

Before joining UIC, Lan Zhang was an Assistant Professor (2001-2005) and Associate Professor (effective 2006) at Carnegie Mellon University. At UIC, She became a tenured Associate Professor  in 2008 and Professor in 2010. She was Reader (2009-2010) at the University of Oxford, UK (Said School of Business, and Oxford Man Institute of Quantitative Finance), as well as fellow of St. Edmund Hall College. She was Visiting Professor at the University of Oslo (2016-2017). 

 

Zoom:

https://zoom.us/j/82957013639?pwd=bDIvTzJEbFFVSXk0Z2JWKzhkdk9Sdz09