Modeling and Forecasting Realized Volatility

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.KEYWORDS: Continuous-time methods, quadratic variation, realized volatility, realized correlation, highfrequency data, exchange rates, vector autoregression, long memory, volatility forecasting, correlation forecasting, density forecasting, risk management, value at risk. _________________ * This paper supercedes the earlier manuscript "Forecasting Volatility: A VAR for VaR." The work reported in the paper was supported by the National Science Foundation. We are grateful to Olsen and Associates, who generously made available their intraday exchange rate quotation data. For insightful suggestions and comments we thank Rob Engle, Atsushi Inoue, Neil Shephard, Clara Vega, Sean Campbell, and seminar participants at Chicago, Michigan, Montreal/CIRANO, NYU, Rice, and the June 2000 Meeting of the Western Finance Association. and covariances (or correlations). When important, the precise meaning will be clear from context.

Deja Vol: Predictive Regressions for Aggregate Stock Market Volatility Using Macroeconomic Variables

“…(1) and the realized variance literature that employs intraday returns to measure return variation. Andersen, Bollerslev, Diebold, and Labys (2003) and Barndorff-Nielsen and Shephard (2002) show that, as the intraperiod sampling frequency increases, Eq. (1) converges in probability to the quadratic variation of a frictionless, arbitrage-free asset price process.…”

Do Co-Jumps Impact Correlations in Currency Markets?

“…A usual first step to build the estimator of quadratic covariation is to consider the realized covariance (Andersen et al, 2003;Barndorff-Nielsen and Shephard, 2004a) that can be estimated over a fixed time…”

Coupling High-Frequency Data with Nonlinear Models in Multiple-Step-Ahead Forecasting of Energy Markets' Volatility

“…Popular heterogeneous autoregressive (HAR) models and autoregressive fractionally integrated (ARFIMA) models became widely used to forecast the realized volatility because they capture the long memory property of the volatility well (Corsi, 2009;Andersen et al, 2003). In contrast to FI-GARCH models capturing the long memory of volatility using daily returns data, 4 these approaches are more flexible and easier to estimate once we have high-frequency data available.…”

“…3 Andersen and Bollerslev (1998); Andersen et al (2001Andersen et al ( , 2003; Zhang et al (2005); Bandi and Russell (2006); Hansen and Lunde (2006); Barndorff-Nielsen et al (2008). 4 Kang and Yoon (2013) recently investigate the ability of FIGARCH models to capture the volatility of energy markets.…”