Parametric and Nonparametric Volatility Measurement

Torben G. Andersen*, Tim Bollersley, Francis X. Diebold

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

106 Scopus citations

Abstract

This chapter provides a unified continuous-time, frictionless, no-arbitrage framework for systematically categorizing the various volatility concepts, measurement procedures, and modeling procedures. Volatility has been one of the most active areas of research in empirical finance and time series econometrics during the past decade. It defines different volatility concepts; the notional volatility corresponding to the sample-path return variability over a fixed time interval; the expected volatility over a fixed time interval; and the instantaneous volatility corresponding to the strength of the volatility process at a point in time. The parametric procedures rely on explicit functional form assumptions regarding the expected and/or instantaneous volatility. In the discrete-time ARCH class of models, the expectations are formulated in terms of directly observable variables, while the discrete and continuous-time stochastic volatility models involve latent state variable(s). The nonparametric procedures are generally free from such functional form assumptions and hence afford estimates of notional volatility that are flexible yet consistent (as the sampling frequency of the underlying returns increases). The nonparametric procedures include ARCH filters and smoothers designed to measure the volatility over infinitesimally short horizons, as well as the recently popularized realized volatility measures for fixed-length time intervals.

Original languageEnglish (US)
Title of host publicationHandbook of Financial Econometrics, Vol 1
PublisherElsevier Inc
Pages67-137
Number of pages71
ISBN (Print)9780444508973
DOIs
StatePublished - Dec 1 2010

ASJC Scopus subject areas

  • Economics, Econometrics and Finance(all)

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    Andersen, T. G., Bollersley, T., & Diebold, F. X. (2010). Parametric and Nonparametric Volatility Measurement. In Handbook of Financial Econometrics, Vol 1 (pp. 67-137). Elsevier Inc. https://doi.org/10.1016/B978-0-444-50897-3.50005-5