英文标题：
《Implied volatility in strict local martingale models》
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作者：
Antoine Jacquier and Martin Keller-Ressel
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最新提交年份：
2015
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英文摘要：
We consider implied volatilities in asset pricing models, where the discounted underlying is a strict local martingale under the pricing measure. Our main result gives an asymptotic expansion of the right wing of the implied volatility smile and shows that the strict local martingale property can be determined from this expansion. This result complements the well-known asymptotic results of Lee and Benaim-Friz, which apply only to true martingales. This also shows that `price bubbles\' in the sense of strict local martingale behaviour can in principle be detected by an analysis of implied volatility. Finally we relate our results to left-wing expansions of implied volatilities in models with mass at zero by a duality method based on an absolutely continuous measure change.
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中文摘要：
我们考虑了资产定价模型中的隐含波动率，其中在定价测度下，贴现的基础是严格的局部鞅。我们的主要结果给出了隐含波动率微笑右翼的渐近展开式，并表明严格的局部鞅性质可以由该展开式确定。这个结果补充了Lee和Benaim Friz的著名渐近结果，后者仅适用于真鞅。这也表明，严格的局部鞅行为意义上的“价格泡沫”原则上可以通过对隐含波动率的分析来发现。最后，我们通过基于绝对连续测量变化的对偶方法，将我们的结果与质量为零的模型中隐含波动率的左翼展开联系起来。
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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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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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