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2012 | OriginalPaper | Chapter

8. Modelling High-Frequency Volatility

Author : Professor Dr. Nikolaus Hautsch

Published in: Econometrics of Financial High-Frequency Data

Publisher: Springer Berlin Heidelberg

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Abstract

>This chapter discusses different ways to estimate intraday volatility. Section 8.1 presents realized measures to estimate intraday quadratic variation. Here, we compactly illustrate fundamental approaches, such as the maximum likelihood estimator by Aït-Sahalia et al. (2005), the realized kernel estimator by Barndorff-Nielsen et al. (2008a) as well as the pre-averaging estimator by Jacod et al. (2009). We restrict ourselves to a rather intuitive discussion of the major principles behind these estimators. A more in-depth treatment, however, is beyond the scope of this book and we refer to the reader to the underlying literature.

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previous chapter Vector Multiplicative Error Models

next chapter Estimating Market Liquidity

In the literature it is often also called realized volatility though in a strict sense, the terminology “volatility” is typically used for σ_t rather than for σ_t ².

All estimators are correspondingly scaled in order to account for “border effects” when the sampling grid does not exactly match the underlying sampling period.

Note that the p-values of the GARCH-RV model have to be interpreted with care since the process depends on pre-estimated regressors. Computing exact standard errors requires taking the sampling error of the pre-averaging estimator explicitly account. A deeper discussion of these effects is beyond the scope of this illustration.

To reduce the potential effects of outliers, Pagan and Schwert (1990) suggest replacing the variables in 8.29 by their corresponding logarithmic transformations.

For the ease of exposition, no log returns are used. However, using log returns would not change the general proceeding.

See, e.g., Andersen and Bollerslev (1998a,b) for further references.

In this context, it is common to approximate p(t) by the most recent observed price before t.

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Title: Modelling High-Frequency Volatility
Author: Professor Dr. Nikolaus Hautsch
Publisher: Springer Berlin Heidelberg
Book: Econometrics of Financial High-Frequency Data
Print ISBN: 978-3-642-21924-5

Electronic ISBN: 978-3-642-21925-2

Copyright Year: 2012
DOI: https://doi.org/10.1007/978-3-642-21925-2_8