02675cam a22002657 4500001000600000003000500006005001700011008004100028100002400069245013800093260006600231490005100297500001700348520151900365530006101884538007201945538003602017690011002053700002102163700002402184710004202208830008602250856003702336856003602373t0279NBER20140921135251.0140921s2002 mau||||fs|||| 000 0 eng d1 aAndersen, Torben G.10aParametric and Nonparametric Volatility Measurementh[electronic resource] /cTorben G. Andersen, Tim Bollerslev, Francis X. Diebold. aCambridge, Mass.bNational Bureau of Economic Researchc2002.1 aNBER technical working paper seriesvno. t0279 aAugust 2002.3 aVolatility 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC1 - Econometric and Statistical Methods and Methodology: General2Journal of Economic Literature class.1 aBollerslev, Tim.1 aDiebold, Francis X.2 aNational Bureau of Economic Research. 0aTechnical Working Paper Series (National Bureau of Economic Research)vno. t0279.4 uhttp://www.nber.org/papers/t027941uhttp://dx.doi.org/10.3386/t0279