摘要翻译：
我们颠倒布莱克-斯科尔斯公式。我们考虑低罢工、大罢工、短到期和大到期的情况。我们明确地给出了展开式的前5项。文中还给出了用归纳法计算所有项的方法。在货币，我们有一个封闭形式的公式，隐含的对数正态波动率表示的幂级数在看涨价格。
---
英文标题：
《Asymptotic Expansions of the Lognormal Implied Volatility : A Model Free
  Approach》
---
作者：
Cyril Grunspan
---
最新提交年份：
2011
---
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
--

---
英文摘要：
  We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At the money, we have a closed form formula for implied lognormal volatility in terms of a power series in call price.
---
PDF链接：
https://arxiv.org/pdf/1112.1652