摘要翻译：
我们回顾并说明了波动微笑是如何转化为概率分布的，市场隐含的概率分布代表了价格中的信念。研究了微笑变化的影响。特别注意斜率的影响，它可能会出现在最初的反直觉。然后我们展示了如何使用贝叶斯方法来处理稀疏的真实市场数据。对于参数模型中的每一个偏斜，我们都关联了一个概率。通过一个例子说明了这一点，并导出了多元参数分布。我们引入模糊微笑（或模糊歪斜）作为歪斜分布的可视化说明。
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英文标题：
《Market Implied Probability Distributions and Bayesian Skew Estimation》
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作者：
Ulrich Kirchner
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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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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
  We review and illustrate how the volatility smile translates into a probability distribution, the market-implied probability distribution representing believes priced in. The effects of changes in the smile are examined. Special attention is given to the effects of slope, which might appear at first counter-intuitive.   We then show how Bayesian methods can be used to deal with sparse real market data. With each skew in a parametric model we associate a probability. This is illustrated with an example, for which multivariate parameter distributions are derived. We introduce the fuzzy smile (or fuzzy skew) as a visual illustration of the skew distribution.
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PDF链接：
https://arxiv.org/pdf/0911.0805