Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractThe increasing availability of financial market data at intraday frequencies has not only led to the development of improved volatility measurements but has also inspired research into their potential value as an information source for volatility forecasting. In this paper we explore the forecasting value of historical volatility (extracted from daily return series), of implied volatility (extracted from option pricing data) and of realised volatility (computed as the sum of squared high frequency returns within a day). First we consider unobserved components and long memory models for realised volatility which is regarded as an accurate estimator of volatility. The predictive abilities of realised volatility models are compared with those of stochastic volatility models and generalised autoregressive conditional heteroskedasticity models for daily return series. These historical volatility models are extended to include realised and implied volatility measures as explanatory variables for volatility. The main focus is on forecasting the daily variability of the Standard & Poor's 100 stock index series for which trading data (tick by tick) of almost seven years is analysed. The forecast assessment is based on the hypothesis of whether a forecast model is outperformed by alternative models. In particular, we will use superior predictive ability tests to investigate the relative forecast performances of some models. Since volatilities are not observed, realised volatility is taken as a proxy for actual volatility and is used for computing the forecast error. A stationary bootstrap procedure is required for computing the test statistic and its p-value. The empirical results show convincingly that realised volatility models produce far more accurate volatility forecasts compared to models based on daily returns. Long memory models seem to provide the most accurate forecasts.JEL classification: C22, C53, G15.

Forecasting crude oil market volatility: Further evidence using GARCH-class models

“…As shown in Table 1, the sample mean of crude oil returns is quite small in comparison with its standard deviation (volatility); thus, we set the conditional mean μ t to equal 0 in this paper, following Koopman et al (2005), among others. Another linear GARCH-class model is the IGARCH model developed by Engle and Bollerslev (1986), which can capture infinite persistence in the conditional variance.…”

Asymmetry, realised volatility and stock return risk estimates

“…whereσ 2 T is the value of realised volatility at T andδ is the quasi-maximum likelihood estimate of δ (see Koopman et al 2005). Similar expressions of the one-day-ahead variance forecasts for the other models can be deduced.…”

“…In this paper, we use the 5-min squared returns (from www.price-data.com) to calculate the measure of realised volatility proposed by Martens (2002) (15) contain, respectively, the values of the modified LjungBox statistic for the return series and for the squared return series. * means that the corresponding value is significant at a 5% significance level and used in Koopman et al (2005), that consists on scaling the sum of 5-min returns byσ…”

On Forecasting Taiwanese Stock Index Option Prices: The Role of Implied Volatility Index

“…We deal with two economic loss functions. Koopman et al (2005) compare the predictive ability of historical volatility (extracted from daily returns), implied volatility (extracted from option data) and realized volatility (the cumulative sum of squared high frequency returns within a day) for forecasting daily variability of the S&P 100 stock index returns. Corrado and Truong (2007) augment the GJR-GARCH model of Glosten et al (1993) by intraday high-low price range and VIX in order to investigate their additional information for improving GJR-GARCH volatility forecasting accuracy.…”