Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high-frequency index returns

Abstract

The information content of implied volatilities and intraday returns is compared, in the context of forecasting index volatility over horizons from 1 to 20 days. Forecasts of two measures of realised volatility are obtained after estimating ARCH models using daily index returns, daily observations of the VIX index of implied volatility and sums of squares of 5-min index returns. The in-sample estimates show that nearly all relevant information is provided by the VIX index and hence there is not much incremental information in high-frequency index returns. For out-of-sample forecasting, the VIX index provides the most accurate forecasts for all forecast horizons and performance measures considered. The evidence for incremental forecasting information in intraday returns is insignificant.

Introduction

The ability of ARCH models to provide good estimates of equity return volatility is well documented. Many studies show that the parameters of a variety of different ARCH models are highly significant in-sample; see Bollerslev (1987), Nelson (1991), Glosten et al. (1993) and surveys by Bollerslev et al. (1992), Bera and Higgins (1993) and Bollerslev et al. (1994).

There is less evidence that ARCH models provide good forecasts of equity return volatility. Some studies (Akgiray, 1989; Heynen and Kat, 1994; Franses and Van Dijk, 1995; Brailsford and Faff, 1996; Figlewski, 1997) examine the out-of-sample predictive ability of ARCH models, with mixed results. All find that a regression of realised volatility on forecast volatility produces a low R² statistic (often less than 10%) and hence the predictive power of the forecasts may be questionable. Dimson and Marsh (1990) show that data snooping can produce enhanced in-sample predictive ability that is not transferable to out-of-sample forecasting. Nelson (1992) uses theoretical methods to show that the predictive ability of ARCH models is very good at high frequencies, even when the model is misspecified, but that out-of-sample forecasting of medium- to long-term volatility can be poor. Nelson and Foster (1995) develop conditions for ARCH models to perform favourably at medium- to long-term forecast horizons.

An alternative to ARCH volatility forecasts is to use implied volatilities from options. These are known to covary with realised volatility (Latane and Rendleman, 1976; Chiras and Manaster, 1978) and hence it is of interest to compare the forecasting accuracy of ARCH with implied volatility. To do this many studies use S&P 100 index options which are American. Day and Lewis (1992) find that implied volatilities perform as well but no better than forecasts from ARCH models. Mixtures of the two forecasts outperform both univariate forecasts. Canina and Figlewski (1993) provide contrary evidence to Day and Lewis. They find that implied volatilities are poor forecasts of volatility and that simple historical volatilities outperform implied volatilities. Christensen and Prabhala (1998) show for a much longer period that while implied volatilities are biased forecasts of volatility they outperform historical information models when forecasting volatility.

These papers use implied volatilities that contain measurement errors, because early exercise is ignored and/or dividends are ignored and/or the spot index contains stale prices. The implied volatility series are potentially flawed and this may account for some of the conflicting results. Fleming et al. (1995) describe an implied volatility index (VIX) which eliminates mis-specification problems. We use the same index to obtain new results about the information content of option prices. Fleming (1998) uses a volatility measure similar to VIX to show that implieds outperform historical information.

From the recent studies of Christensen and Prabhala (1998) and Fleming (1998) it can be concluded that the evidence now favours the conclusion that implied volatilities are more informative than daily returns when forecasting equity volatility. The same conclusion has been obtained for foreign exchange volatility from daily data, but with more certainty (Jorion, 1995; Xu and Taylor, 1995). High-frequency returns, however, have the potential to change these conclusions. Taylor and Xu (1997) show that 5-min FX returns contain volatility information incremental to that provided by options. In this paper we explore the incremental volatility information of high-frequency stock index returns for the first time.

The importance of intraday returns for measuring realised volatility is demonstrated for FX data by Taylor and Xu (1997), Andersen and Bollerslev (1998) and Andersen et al. (2001b), and for equities by Ebens (1999) and Andersen et al. (2001a). Andersen and Bollerslev (1998) prove that regression methods will give low R² values when daily squared returns measure realised volatility, even for optimal GARCH forecasts, because squared returns are noisy estimates of volatility. They show that intraday returns can be used to construct a realised volatility series that essentially eliminates the noise in measurements of daily volatility. They find remarkable improvements in the forecasting performance of ARCH models for FX data when they are used to forecast the new realised series, compatible with theoretical analysis. They do not, however, compare ARCH forecasts with implied forecasts.

This paper answers some important empirical questions for the S&P 100 index. Firstly, how does the predictive quality of volatility forecasts from ARCH models, that use daily index returns and/or intraday returns, compare with forecasts from models that use information contained in implied volatilities? Secondly, how important is the selection of the measure of realised volatility in assessing the predictive accuracy of volatility forecasts?

The paper is arranged as follows. Section 2 discusses the various data sets we use and issues surrounding their construction. Methods for estimating and forecasting volatility that use daily index returns, 5-min returns and implied volatilities are presented in Section 3. Section 4 provides results from both in-sample estimation and out-of-sample forecasting of S&P 100 volatility. Section 5 sets out our conclusions.