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摘要翻译：
本文研究了局部波动率模型中正态隐含波动率的动态特性，在此展开式的前序处，正态隐含波动率的渐近性与对数正态波动率的渐近性相似，直到不同的货币性定义为止。这种关系在小时间展开式中也保持为O(T)级，在O(T^2)处首先出现与对数正态情形的差异。在几个具有解析局部波动率的局部波动率模型的例子上说明了结果，发现通常与精确解或数值解很好地吻合。我们指出，对于具有非分析局部波动性的模型，例如具有不连续导数的模型，如果简单地应用渐近展开式可能会失败。利用扰动理论的方法，我们证明了这类模型的ATM正态隐含波动率包含一项~\sqrt{T}，其系数与导数的跳跃成正比。
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英文标题：
《Asymptotic Expansion for the Normal Implied Volatility in Local
Volatility Models》
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作者：
Viorel Costeanu and Dan Pirjol
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最新提交年份：
2011
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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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 study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the asymptotics of the normal implied volatility is similar, up to a different definition of the moneyness, to that of the log-normal volatility. This relation is preserved also to order O(T) in the small-time expansion, and differences with the log-normal case appear first at O(T^2). The results are illustrated on a few examples of local volatility models with analytical local volatility, finding generally good agreement with exact or numerical solutions. We point out that the asymptotic expansion can fail if applied naively for models with nonanalytical local volatility, for example which have discontinuous derivatives. Using perturbation theory methods, we show that the ATM normal implied volatility for such a model contains a term ~ \sqrt{T}, with a coefficient which is proportional with the jump of the derivative.
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PDF链接：
https://arxiv.org/pdf/1105.3359
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