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Parametric and Nonparametric Volatility Measurement

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Author Info
Torben G. Andersen
Tim Bollerslev
Francis X. Diebold

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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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0279.

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Date of creation: Aug 2002
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Handle: RePEc:nbr:nberte:0279

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C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General

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  15. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Vega, Clara, 2002. "Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange," Working Papers 02-16, Duke University, Department of Economics. [Downloadable!]
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  27. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August. [Downloadable!] (restricted)
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  32. Torben G. Andersen & Tim Bollerslev, 1998. "Deutsche Mark-Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies," Journal of Finance, American Finance Association, vol. 53(1), pages 219-265, 02. [Downloadable!] (restricted)
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  44. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July. [Downloadable!] (restricted)
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