Parametric and Nonparametric Volatility Measurement

68 Pages Posted: 18 Aug 2002

See all articles by Torben G. Andersen

Torben G. Andersen

Northwestern University - Kellogg School of Management; National Bureau of Economic Research (NBER); Aarhus University - CREATES

Tim Bollerslev

Duke University - Finance; Duke University - Department of Economics; National Bureau of Economic Research (NBER)

Francis X. Diebold

University of Pennsylvania - Department of Economics; National Bureau of Economic Research (NBER)

Multiple version iconThere are 2 versions of this paper

Date Written: August 2002

Abstract

Volatility has been one of the most active areas of research in empirical finance and time series econometrics during the past decade. This chapter provides a unified continuous-time, frictionless, no-arbitrage framework for systematically categorizing the various volatility concepts, measurement procedures, and modeling procedures. We define three different volatility concepts: (i) the notional volatility corresponding to the ex-post sample-path return variability over a fixed time interval, (ii) the ex-ante expected volatility over a fixed time interval, and (iii) 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 (non-trivial) fixed-length time intervals.

Suggested Citation

Andersen, Torben G. and Bollerslev, Tim and Diebold, Francis X., Parametric and Nonparametric Volatility Measurement (August 2002). NBER Working Paper No. t0279. Available at SSRN: https://ssrn.com/abstract=324002

Torben G. Andersen (Contact Author)

Northwestern University - Kellogg School of Management ( email )

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Tim Bollerslev

Duke University - Finance ( email )

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Francis X. Diebold

University of Pennsylvania - Department of Economics ( email )

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215-573-4217 (Fax)

HOME PAGE: http://www.ssc.upenn.edu/~fdiebold/

National Bureau of Economic Research (NBER)

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