英文标题：
《Implied and Realized Volatility: A Study of Distributions and the
Distribution of Difference》
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作者：
M. Dashti Moghaddam, Jiong Liu and R. A. Serota
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最新提交年份：
2019
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英文摘要：
We study distributions of realized variance (squared realized volatility) and squared implied volatility, as represented by VIX and VXO indices. We find that Generalized Beta distribution provide the best fits. These fits are much more accurate for realized variance than for squared VIX and VXO -- possibly another indicator that the latter have deficiencies in predicting the former. We also show that there are noticeable differences between the distributions of the 1970-2017 realized variance and its 1990-2017 portion, for which VIX and VXO became available. This may be indicative of a feedback effect that implied volatility has on realized volatility. We also discuss the distribution of the difference between squared implied volatility and realized variance and show that, at the basic level, it is consistent with Pearson\'s correlations obtained from linear regression.
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中文摘要：
我们研究了以VIX和VXO指数表示的已实现方差（已实现波动率平方）和隐含波动率平方的分布。我们发现，广义Beta分布提供了最佳拟合。对于已实现方差，这些拟合要比平方VIX和VXO准确得多，这可能是后者在预测前者方面存在缺陷的另一个指标。我们还表明，1970-2017年实现方差的分布与其1990-2017年部分之间存在显著差异，其中VIX和VXO可用。这可能表明隐含波动率对已实现波动率具有反馈效应。我们还讨论了平方隐含波动率和已实现方差之间的差异分布，并表明在基本水平上，它与线性回归得到的Pearson相关性是一致的。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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