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摘要翻译：
本文研究了指数L\'evy型股票价格模型中欧式看涨期权的小到期行为。在大多数感兴趣的情况下，我们能够识别精确的小过期渐近。在“完全概括性”中，我们能够证明当\tau（到期时间）为零时，看涨期权的时间价值有O(\tau)衰减。利用我们对接近到期的看涨期权行为的研究结果，我们发现在“大多数”指数L\'evy模型中，隐含波动率以$\tau\to0^+$的形式爆炸。注意力仅限于调用和隐含的不在金钱上的挥发。
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英文标题：
《Implied volatility explosions: European calls and implied volatilities
close to expiry in exponential L\'evy models》
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作者：
Michael Roper
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最新提交年份：
2008
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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 examine the small expiry behaviour of European call options in stock price models of exponential L\'evy type. In most cases of interest, we are able to identify the exact small expiry asymptotics. In "complete generality" we are able to show that the time value of the call option has O(\tau) decay as \tau (time to expiry) goes to zero. Using our results on the behaviour of call options close to expiry we show that implied volatility explodes as $\tau\to0^+$ in "most" exponential L\'evy models. Attention is restricted to calls and implied volatilities that are not at-the-money.
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PDF链接：
https://arxiv.org/pdf/0809.3305
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