摘要翻译：
我们研究了Black-Scholes隐含波动率的特殊非线性变换，以显示波动率面的显著性质。给出了隐含波动率偏差的无模型界。给出了用隐含波动率表示的欧式期权定价公式。特别地，我们证明了方差交换和伽玛交换的公平罢工的优雅公式。
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英文标题：
《Normalization for Implied Volatility》
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作者：
Masaaki Fukasawa
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最新提交年份：
2010
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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：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
  We study specific nonlinear transformations of the Black-Scholes implied volatility to show remarkable properties of the volatility surface. Model-free bounds on the implied volatility skew are given. Pricing formulas for the European options which are written in terms of the implied volatility are given. In particular, we prove elegant formulas for the fair strikes of the variance swap and the gamma swap.
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PDF链接：
https://arxiv.org/pdf/1008.5055