英文标题：
《Shapes of implied volatility with positive mass at zero》
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作者：
Stefano De Marco, Caroline Hillairet, Antoine Jacquier
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最新提交年份：
2017
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英文摘要：
We study the shapes of the implied volatility when the underlying distribution has an atom at zero and analyse the impact of a mass at zero on at-the-money implied volatility and the overall level of the smile. We further show that the behaviour at small strikes is uniquely determined by the mass of the atom up to high asymptotic order, under mild assumptions on the remaining distribution on the positive real line. We investigate the structural difference with the no-mass-at-zero case, showing how one can--theoretically--distinguish between mass at the origin and a heavy-left-tailed distribution. We numerically test our model-free results in stochastic models with absorption at the boundary, such as the CEV process, and in jump-to-default models. Note that while Lee\'s moment formula tells that implied variance is at most asymptotically linear in log-strike, other celebrated results for exact smile asymptotics such as Benaim and Friz (09) or Gulisashvili (10) do not apply in this setting--essentially due to the breakdown of Put-Call duality.
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中文摘要：
我们研究了当基础分布中原子为零时隐含波动率的形状，并分析了质量为零时对货币隐含波动率和微笑总体水平的影响。我们进一步证明，在对正实线上剩余分布的温和假设下，小碰撞时的行为唯一地由高渐近阶的原子质量决定。我们研究了零质量情况下的结构差异，从理论上讲，我们可以区分原点的质量和重左尾分布。我们在边界有吸收的随机模型（如CEV过程）和跳转到默认模型中对我们的无模型结果进行了数值测试。请注意，虽然Lee的矩公式告诉我们，在对数走向中，隐含方差最多是渐近线性的，但其他著名的精确微笑渐近结果，如Benaim和Friz（09）或Gulisashvili（10）不适用于这种情况——这主要是由于Put-Call对偶性的崩溃。
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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：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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