Yazhen Wang
National Science Foundation
Title: Volatility Matrix Estimation for High-Frequency Financial Data
Abstract:
High-frequency data observed on the prices of financial assets are
commonly modeled by diffusion processes with micro-structure noise, and
realized volatility based methods are often used to estimate integrated
volatility.
For problems involving with a large number of assets, the estimation
objects we face are volatility matrices of large size. The existing
volatility estimators work well for a small number of assets but
perform poorly when the number of assets is very large. In fact, they
are inconsistent when both the number, $p$, of the assets and the
average sample size, $n$, of the price data on the $p$ assets go to
infinity. In this talk I will present a new type of estimators for the
integrated volatility matrix and describe asymptotic theory for the
proposed estimators in the framework that allows both $n$ and $p$ to
approach to infinity.
The theory shows that the proposed estimators achieve high convergence
rates under a sparsity assumption on the integrated volatility matrix.
The numerical studies demonstrate that the proposed estimators perform
well for large $p$ and complex price and volatility models.