TY - JOUR
AU - Andersen,Torben G.
AU - Bollerslev,Tim
AU - Diebold,Francis X.
TI - Parametric and Nonparametric Volatility Measurement
JF - National Bureau of Economic Research Technical Working Paper Series
VL - No. 279
PY - 2002
Y2 - August 2002
UR - http://www.nber.org/papers/t0279
L1 - http://www.nber.org/papers/t0279.pdf
N1 - Author contact info:
Torben G. Andersen
Kellogg School of Management
Northwestern University
2001 Sheridan Road
Evanston, IL 60208
Tel: 847/467-1285
Fax: 847/491-5719
E-Mail: t-andersen@kellogg.northwestern.edu
Tim Bollerslev
Department of Economics
Duke University
Box 90097
Durham, NC 27708-0097
Tel: 919/660-1846
Fax: 919/684-8974
E-Mail: boller@econ.duke.edu
Francis X. Diebold
Department of Economics
University of Pennsylvania
3718 Locust Walk
Philadelphia, PA 19104-6297
Tel: 215/898-1507
Fax: 212/573-4217
E-Mail: fdiebold@sas.upenn.edu
AB - 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.
ER -