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.

Realized Volatility: A Review

“…They showed strong empirical evidence in favor of their proposal. Deo et al (2006) considered a long-memory stochastic volatility model and Koopman et al (2005) proposed a model combining unobserved components and longmemory. In a recent work, Hillebrand and Medeiros (2008) suggested a model that combines long memory with different types of nonlinearity.…”

Modelling and forecasting multivariate realized volatility

“…With high frequency data, the long persistence in a series of realized volatilities is portrayed by a slow decay in the autocorrelation function (see e.g., Andersen and Bollerslev (1997), Andersen, Bollerslev, Diebold, and Ebens (2001)), and is modeled by means of fractionally integrated ARMA (ARFIMA) processes by Andersen, Bollerslev, Diebold, and Labys (2003), Oomen (2001) and Koopman, Jungbacker, and Hol (2005), among others.…”

Model-Free vs. Model-Based Volatility Prediction

“…by the DurbinLevinson algorithm, also gives an estimate of the prediction error variance σ 2 pred . Note that the simplified expression (17) still represents an unknown quantity but it could conceivably be approximated by Monte Carlo, for example using the normal predictive density that has mean given by (18) and variance σ 2 pred -recall though that this normal density should be truncated to an effective range of ±1/ √ a 0 . However, a very large number of replications would be required due to the heavy tails of the distribution of W 2 / (1 − a 0 W 2 ).…”