英文标题：
《Skew and implied leverage effect: smile dynamics revisited》
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作者：
Vincent Vargas, Tung-Lam Dao, Jean-Philippe Bouchaud
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最新提交年份：
2013
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英文摘要：
  We revisit the ``Smile Dynamics\'\' problem, which consists in relating the implied leverage (i.e. the correlation of the at-the-money volatility with the returns of the underlying) and the skew of the option smile. The ratio between these two quantities, called ``Skew-Stickiness Ratio\'\' (SSR) by Bergomi (Smile Dynamics IV, RISK, 94-100, December 2009), saturates to the value 2 for linear models in the limit of small maturities, and converges to 1 for long maturities. We show that for more general, non-linear models (such as the asymmetric GARCH model), Bergomi\'s result must be modified, and can be larger than 2 for small maturities. The discrepancy comes from the fact that the volatility skew is, in general, different from the skewness of the underlying. We compare our theory with empirical results, using data both from option markets and from the underlying price series, for the S&P500 and the DAX. We find, among other things, that although both the implied leverage and the skew appear to be too strong on option markets, their ratio is well explained by the theory. We observe that the SSR indeed becomes larger than 2 for small maturities.
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中文摘要：
我们重新讨论了“微笑动力学”问题，它包括关联隐含杠杆（即货币波动率与基础收益率的相关性）和期权微笑的倾斜。这两个量之间的比率，由Bergomi（微笑动力学IV，风险，94-1002009年12月）称为“倾斜粘性比率”（SSR），在小期限的限制下，饱和为线性模型的值2，在长期限的限制下收敛为1。我们证明，对于更一般的非线性模型（如非对称GARCH模型），Bergomi的结果必须修改，对于小到期日，Bergomi的结果可以大于2。这种差异来自这样一个事实，即波动率偏差总体上不同于标的资产的偏差。我们使用期权市场和标普500指数和DAX的基础价格序列的数据，将我们的理论与实证结果进行比较。我们发现，除其他外，尽管在期权市场上隐含的杠杆率和倾斜似乎都太强，但它们的比率可以用该理论很好地解释。我们观察到，对于小到期日，SSR确实变得大于2。
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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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