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摘要翻译：
对于给定的时间范围DT，本文从多尺度线性ARCH过程出发，探讨了已实现波动率（t与t+DT之间的波动率）与隐含波动率（对应于t+DT到期的到期日期权）之间的关系，以及对波动率构建的几种预测。预测是从过程方程导出的，参数是先验设定的。对多个时域DT的实证分析表明，由I-GARCH(1)过程（1个时间尺度）提供的预测不能正确地捕捉已实现波动率的动态。I-GARCH(2)过程（两个时间尺度，类似于GARCH(1,1））更好，而长记忆LM-ARCH过程（多个时间尺度）正确地复制了已实现波动率的动态，并对隐含波动率提供了持续良好的预测。研究了正向方差市场模型与ARCH过程提供的波动率预测之间的关系。预测方程的结构相同，但系数不同。然而，方差的过程方程非常不同（市场模型的假设，由ARCH模型的过程方程导出），从ARCH导出时不是任何通常的扩散类型。
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英文标题：
《Volatility forecasts and the at-the-money implied volatility: a
multi-components ARCH approach and its relation with market models》
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作者：
Gilles Zumbach
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最新提交年份：
2009
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
For a given time horizon DT, this article explores the relationship between the realized volatility (the volatility that will occur between t and t+DT), the implied volatility (corresponding to at-the-money option with expiry at t+DT), and several forecasts for the volatility build from multi-scales linear ARCH processes. The forecasts are derived from the process equations, and the parameters set a priori. An empirical analysis across multiple time horizons DT shows that a forecast provided by an I-GARCH(1) process (1 time scale) does not capture correctly the dynamic of the realized volatility. An I-GARCH(2) process (2 time scales, similar to GARCH(1,1)) is better, while a long memory LM-ARCH process (multiple time scales) replicates correctly the dynamic of the realized volatility and delivers consistently good forecast for the implied volatility. The relationship between market models for the forward variance and the volatility forecasts provided by ARCH processes is investigated. The structure of the forecast equations is identical, but with different coefficients. Yet the process equations for the variance are very different (postulated for a market model, induced by the process equations for an ARCH model), and not of any usual diffusive type when derived from ARCH.
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PDF链接：
https://arxiv.org/pdf/0901.2275
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