Volatility Forecasting With Range-Based EGARCH Models

We provide a simple, yet highly effective framework for forecasting return volatility by combining exponential generalized autoregressive conditional heteroscedasticity models with data on the range. Using Standard and Poor's 500 index data for 1983–2004, we demonstrate the importance of a long-memory specification, based on either a two-factor structure or fractional integration, that allows for some asymmetry between market returns and volatility innovations. Out-of-sample forecasts reinforce the value of both this specification and the use of range data in the estimation. We find substantial forecastability of volatility as far as 1 year from the end of the estimation period, contradicting the return-based conclusions of West and Cho and of Christoffersen and Diebold that predicting volatility is possible only for short horizons.

[1]  W. Feller.  The Asymptotic Distribution of the Range of Sums of Independent Random Variables , 1951 .

[2]  M. Parkinson.  The Extreme Value Method for Estimating the Variance of the Rate of Return , 1980 .

[3]  M. J. Klass,et al.  On the Estimation of Security Price Volatilities from Historical Data , 1980 .

[4]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[5]  A. Christie,et al.  The stochastic behavior of common stock variances: value , 1982 .

[6]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[7]  K. French,et al.  Stock return variances: The arrival of information and the reaction of traders , 1986 .

[8]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[9]  K. French,et al.  Expected stock returns and volatility , 1987 .

[10]  T. Bollerslev,et al.  A CONDITIONALLY HETEROSKEDASTIC TIME SERIES MODEL FOR SPECULATIVE PRICES AND RATES OF RETURN , 1987 .

[11]  Adrian Pagan,et al.  Alternative Models for Conditional Stock Volatility , 1989 .

[12]  M. Yor,et al.  Continuous martingales and Brownian motion , 1990 .

[13]  G. William Schwert,et al.  Stock Volatility and the Crash , 1990 .

[14]  John Y. Campbell,et al.  No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns , 1991 .

[15]  Robert F. Engle,et al.  Stock Volatility and the Crash of '87: Discussion , 1990 .

[16]  Gautam Kaul,et al.  Asymmetric Predictability of Conditional Variances , 1991 .

[17]  L. Rogers,et al.  Estimating Variance From High, Low and Closing Prices , 1991 .

[18]  Daniel B. Nelson.  CONDITIONAL HETEROSKEDASTICITY IN ASSET RETURNS: A NEW APPROACH , 1991 .

[19]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[20]  K. West,et al.  The Predictive Ability of Several Models of Exchange Rate Volatility , 1994 .

[21]  F. Diebold,et al.  Comparing Predictive Accuracy , 1994, Business Cycles.

[22]  Peter E. Rossi,et al.  Bayesian Analysis of Stochastic Volatility Models , 1994 .

[23]  W. Newey,et al.  Automatic Lag Selection in Covariance Matrix Estimation , 1994 .

[24]  Bent E. Sørensen,et al.  GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study , 1996 .

[25]  T. Bollerslev,et al.  MODELING AND PRICING LONG- MEMORY IN STOCK MARKET VOLATILITY , 1996 .

[26]  Bent E. Sørensen,et al.  GMM and QML asymptotic standard deviations in stochastic volatility models: Comments on Ruiz (1994) , 1997 .

[27]  T. Bollerslev,et al.  ANSWERING THE SKEPTICS: YES, STANDARD VOLATILITY MODELS DO PROVIDE ACCURATE FORECASTS* , 1998 .

[28]  A. Gallant,et al.  Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance , 1999, Review of Economics and Statistics.

[29]  D. Yang,et al.  Drift Independent Volatility Estimation Based on High, Low, Open, and Close Prices , 2000 .

[30]  Andrew Ang,et al.  Asymmetric Correlations of Equity Portfolios , 2001 .

[31]  F. Longin,et al.  Extreme Correlation of International Equity Markets , 2000 .

[32]  F. Diebold,et al.  How Relevant is Volatility Forecasting for Financial Risk Management? , 1997, Review of Economics and Statistics.

[33]  Michael W. Brandt,et al.  Range-Based Estimation of Stochastic Volatility Models , 2001 .

[34]  N. Shephard,et al.  Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics , 2001 .

[35]  F. Diebold,et al.  The distribution of realized stock return volatility , 2001 .

[36]  Michael W. Brandt,et al.  A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations , 2002 .

[37]  T. Bollerslev,et al.  Estimating Stochastic Volatility Diffusion Using Conditional Moments of Integrated Volatility , 2001 .

[38]  Laurent E. Calvet,et al.  Multifractality in Asset Returns: Theory and Evidence , 2002, Review of Economics and Statistics.

[39]  A. Gallant,et al.  Alternative models for stock price dynamics , 2003 .

[40]  R. Chou,et al.  Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model , 2005 .

[41]  William B. White,et al.  All in the Family , 2005 .

[42]  Peter F. Christoffersen,et al.  Option Valuation with Long-Run and Short-Run Volatility Components , 2008 .