Forecasting Daily Variability of the S&P 100 Stock Index Using Historical, Realised and Implied Volatility Measurements
Forecasting Daily Variability of the S&P 100 Stock Index Using Historical, Realised and Implied Volatility Measurements
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DOI：
10.2139/ssrn.499744
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发表时间：
2004-01
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影响因子：
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通讯作者：
S. J. Koopman;Borus Jungbacker;Eugenie Hol Uspensky
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文献类型：
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作者：
S. J. Koopman;Borus Jungbacker;Eugenie Hol Uspensky
这篇论文发表在《经验金融学杂志》（Journal of Empirical Finance，2005年）上。第12卷，第3期，第445-475页。日内金融市场数据的可获得性日益增加，不仅导致了波动性计量方法的改进，而且也激发了对波动性预测信息来源的潜在价值的研究。在本文中，我们探讨的预测价值的历史波动率（从每日收益率序列中提取），隐含波动率（从期权定价数据中提取）和已实现的波动率（计算为一天之内的高频回报率的平方和）。首先，我们考虑未观察到的组件和长记忆模型的已实现的波动，这被视为一个准确的估计波动。实现波动率模型的预测能力进行了比较，与随机波动率模型和广义自回归条件异方差模型的每日收益率序列。该等历史波幅模型已扩展至包括已变现及隐含波幅计量，作为波幅的解释变量。主要重点是预测标准普尔100种股票指数系列的每日变化，分析了近七年的交易数据（逐点）。预测评估基于预测模型是否优于替代模型的假设。特别地，我们将使用上级预测能力测试来研究一些模型的相对预测性能。由于没有观察到波动性，因此将已实现波动性作为实际波动性的代表，并用于计算预测误差。一个平稳的引导过程需要计算检验统计量和它的$p$-值。实证结果令人信服地表明，实现波动率模型产生更准确的波动率预测模型的基础上，每日回报。长记忆模型似乎提供了最准确的预测。
This discussion paper resulted in an article in the Journal of Empirical Finance (2005). Vol. 12, issue 3, pages 445-475. The 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.