英文标题：
《On smile properties of volatility derivatives and exotic products:
  understanding the VIX skew》
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作者：
Elisa Al\\`os, David Garc\\\'ia-Lorite and Aitor Muguruza
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最新提交年份：
2018
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英文摘要：
  We develop a method to study the implied volatility for exotic options and volatility derivatives with European payoffs such as VIX options. Our approach, based on Malliavin calculus techniques, allows us to describe the properties of the at-the-money implied volatility (ATMI) in terms of the Malliavin derivatives of the underlying process. More precisely, we study the short-time behaviour of the ATMI level and skew. As an application, we describe the short-term behavior of the ATMI of VIX and realized variance options in terms of the Hurst parameter of the model, and most importantly we describe the class of volatility processes that generate a positive skew for the VIX implied volatility. In addition, we find that our ATMI asymptotic formulae perform very well even for large maturities. Several numerical examples are provided to support our theoretical results.
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中文摘要：
我们发展了一种方法来研究奇异期权和具有欧洲回报的波动率衍生品（如VIX期权）的隐含波动率。我们的方法基于Malliavin演算技术，允许我们根据基础过程的Malliavin导数来描述货币隐含波动率（ATMI）的性质。更准确地说，我们研究了ATMI水平和倾斜的短期行为。作为一个应用，我们根据模型的赫斯特参数描述了波动率指数和已实现方差期权的短期行为，最重要的是，我们描述了波动率过程的类别，该类过程为波动率指数隐含波动率产生正偏斜。此外，我们发现我们的ATMI渐近公式即使对于大型到期债券也表现得很好。文中给出了几个数值例子来支持我们的理论结果。
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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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