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摘要翻译：
利用热核展开式，给出了一种计算随机波动率模型隐含波动率时间泰勒展开式的一般方法。在已知的0级隐含波动率之外，我们根据热核展开的标量系数精确地计算了所有冲击下的一阶修正。此外，热核展开式中的第一次修正给出了隐含波动率的二阶修正，我们也给出了在所有打击下的精确修正。作为应用，我们计算了SABR模型的2阶渐近展开式。
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英文标题：
《Asymptotic Implied Volatility at the Second Order with Application to
the SABR Model》
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作者：
Louis Paulot
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最新提交年份：
2016
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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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英文摘要：
We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kernel expansion. Furthermore, the first correction in the heat kernel expansion gives the second order correction for implied volatility, which we also give exactly at all strikes. As an application, we compute this asymptotic expansion at order 2 for the SABR model.
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PDF链接：
https://arxiv.org/pdf/0906.0658
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