Non-parametric volatility estimation using ultra-high frequency data

Abstract

Purpose of the study

The purpose of the study is to explore the advances made in using ultra-high frequency (UHF) data in estimating and modeling integrated volatility since Andersen & Bollerslev (1998) brought the area into mainstream of volatility research. Use of UHF data with specially constructed non-parametric estimators, called realized estimators, holds great promise for improving the explanatory power of GARCH family models. In addition to a discussion of the various methodologies, the study also contains an empirical part with several realized estimators fitted to GARCH-type models. Previous empirical UHF research has largely focused on extremely liquid stock indices instead of individual stocks: this study focuses on the share price variation of Nokia.

Data

Data for the empirical part of the study comes from the SAXESS trading platform used by the Helsinki Stock Exchange. It includes detailed information of all the trades of Nokia (NOK1V) shares in the exchange between years 2005 and 2009, inclusive. Extensive data cleaning results in 4.1 million unique price observations: one every 9 seconds on average.

Results

The main finding of the study is that employing UHF data and realized estimators lead to much improved volatility estimates. The improvement is larger than the gains from using only more sophisticated GARCH models. Realized measures contain more information about the latent volatility structure and facilitate faster adaptation to new volatility levels. The estimator based on the Parzen kernel function leads to better results than realized variance estimators. Zakoian’s (1993) TARCH model performs the best with realized measures, as well as with the benchmark squared daily return estimator. Even when controlling for the number of free parameters with various information criteria, asymmetric models dominate the symmetric GARCH(1,1) specification.