英文标题：
《Uniform bounds for Black--Scholes implied volatility》
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作者：
Michael R. Tehranchi
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最新提交年份：
2016
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英文摘要：
  In this note, Black--Scholes implied volatility is expressed in terms of various optimisation problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries of the Black--Scholes formula are exploited to derive new bounds from old. These bounds are used to reprove asymptotic formulae for implied volatility at extreme strikes and/or maturities.
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中文摘要：
在本文中，Black-Scholes隐含波动率用各种优化问题表示。从这些表述中，得到了一致适用于货币性和买入价格的上界和下界。利用Black-Scholes公式的各种对称性，从旧公式推导出新的边界。这些界限用于证明极端冲击和/或到期时隐含波动率的渐近公式。
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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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