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Modeling and Forecasting Realized Volatility


Torben G. Andersen


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

Paul Labys


Charles River Associates (CRA) - Utah Office

January 2001

PIER Working Paper No. 01-002

Abstract:     
This paper provides a general framework for integration of high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency volatility and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on restrictive and complicated parametric multivariate ARCH or stochastic volatility models, which often perform poorly at intraday frequencies. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we formally develop the links between the conditional covariance matrix and the concept of realized volatility. Next, using continuously recorded observations for the Deutschemark / Dollar and Yen / Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated density forecasts of future returns, and correspondingly accurate quantile estimates. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.

Number of Pages in PDF File: 47

Keywords: Continuous-Time Methods, Quadratic Variation, Realized Volatility, Realized Correlation, High-Frequency Data, Exchange Rates, Vector Autoregression, Long Memory, Volatility Forecasting, Correlation Forecasting, Density Forecasting, Risk Management, Value at Risk

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Date posted: May 2, 2001  

Suggested Citation

Andersen, Torben G. and Bollerslev, Tim and Diebold, Francis X. and Labys, Paul, Modeling and Forecasting Realized Volatility (January 2001). PIER Working Paper No. 01-002. Available at SSRN: http://ssrn.com/abstract=267792 or http://dx.doi.org/10.2139/ssrn.267792

Contact Information

Torben G. Andersen
Northwestern University - Kellogg School of Management ( email )
2001 Sheridan Road
Evanston, IL 60208
United States
National Bureau of Economic Research (NBER) ( email )
1050 Massachusetts Avenue
Cambridge, MA 02138
United States
University of Aarhus - CREATES ( email )
School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark
Tim Bollerslev
Duke University - Finance ( email )
Durham, NC 27708-0120
United States
919-660-1846 (Phone)
919-684-8974 (Fax)
Duke University - Department of Economics
Durham, NC 27708-0204
United States
National Bureau of Economic Research (NBER)
1050 Massachusetts Avenue
Cambridge, MA 02138
United States
Francis X. Diebold (Contact Author)
University of Pennsylvania - Department of Economics ( email )
3718 Locust Walk
Philadelphia, PA 19104
United States
215-898-1507 (Phone)
215-573-4217 (Fax)
HOME PAGE: http://www.ssc.upenn.edu/~fdiebold/
National Bureau of Economic Research (NBER)
1050 Massachusetts Avenue
Cambridge, MA 02138
United States
Paul Labys
Charles River Associates (CRA) - Utah Office ( email )
170 South Main St., Suite 500
Salt Lake City, UT 84101
United States
801.536.1511 (Phone)
801.536.1501 (Fax)
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