Journal Article

Modeling and Forecasting Realized Volatility

Andersen, Torben G., Diebold, Francis X., Bollerslev, Tim, Labys, Paul

2003

Overview

We provide a framework for integration of high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency return volatilities and return distributions. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we develop formal links between realized volatility and the conditional covariance matrix. Next, using continuously recorded observations for the Deutschemark/Dollar and Yen/Dollar spot exchange rates, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution produces well-calibrated density forecasts of future returns, and correspondingly accurate quantile predictions. 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.

• Publisher: Blackwell Publishing Ltd,Econometric Society,Blackwell
• Subject: American dollar / Analysis of covariance / Applications / Applied sciences / Arbitrage / Asset allocation / Asset pricing / continuous-time methods / Covariance matrices / Data analysis / density forecasting / Econometrics / Economic forecasting / Economic forecasting models / Economic models / Economic theory / Exact sciences and technology / Financial instruments / Forecasting / Forecasting models / Forecasting standards / Forecasts / Foreign exchange rates / high-frequency data / Inference from stochastic processes; time series analysis / Insurance, economics, finance / International finance / long memory / Mathematics / Matrices / Measurement / Memory / Modelling / Operational research and scientific management / Operational research. Management science / Portfolio theory / Probability and statistics / quadratic variation / realized volatility / Regression analysis / Risk management / Risk theory. Actuarial science / Sciences and techniques of general use / Statistical discrepancies / Statistical forecasts / Statistics / Stochastic models / Studies / Time series forecasting / Vector autoregression / Volatility / volatility forecasting