英文标题：
《Distributions of Historic Market Data -- Implied and Realized Volatility》
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作者：
M. Dashti Moghaddam, Zhiyuan Liu, R. A. Serota
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最新提交年份：
2018
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英文摘要：
We undertake a systematic comparison between implied volatility, as represented by VIX (new methodology) and VXO (old methodology), and realized volatility. We compare visually and statistically distributions of realized and implied variance (volatility squared) and study the distribution of their ratio. We find that the ratio is best fitted by heavy-tailed -- lognormal and fat-tailed (power-law) -- distributions, depending on whether preceding or concurrent month of realized variance is used. We do not find substantial difference in accuracy between VIX and VXO. Additionally, we study the variance of theoretical realized variance for Heston and multiplicative models of stochastic volatility and compare those with realized variance obtained from historic market data.
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中文摘要：
我们对以VIX（新方法）和VXO（旧方法）为代表的隐含波动率和已实现波动率进行了系统比较。我们比较了已实现方差和隐含方差（波动率平方）的视觉和统计分布，并研究了它们的比率分布。我们发现，该比率最好由重尾分布（对数正态分布和厚尾分布（幂律分布））拟合，这取决于使用的是前一个月还是同时使用的已实现方差。我们没有发现VIX和VXO之间的精度有实质性差异。此外，我们还研究了赫斯顿和随机波动率乘法模型的理论实现方差的方差，并将其与从历史市场数据中获得的实现方差进行了比较。
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分类信息：

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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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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