摘要翻译：
在指数L\'evy模型中，研究了标的股票以连续利率支付股利时，美式看跌期权临近到期时临界价格的行为。特别地，我们证明了在临界价格的极限等于股票价格的情况下，收敛到极限的速度是线性的当且仅当潜在的L\'Evy过程有有限变差。在无限变分的情况下，可以观察到各种收敛速度：我们证明了当L\\evy测度的负部分在原点附近呈现$\\alpha$-稳定密度时，当$1<\alpha<2$时，收敛速度由$\theta^{1/\alpha}\ln\theta^{1-\frac{1}{\alpha}}$决定，其中$\theta$是直到成熟的时间。
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英文标题：
《Exercise Boundary of the American Put Near Maturity in an Exponential
  L\'evy Model》
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作者：
Damien Lamberton and Mohammed Mikou
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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：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 behavior of the critical price of an American put option near maturity in the exponential L\'evy model when the underlying stock pays dividends at a continuous rate. In particular, we prove that, in situations where the limit of the critical price is equal to the stock price, the rate of convergence to the limit is linear if and only if the underlying L\'evy process has finite variation. In the case of infinite variation, a variety of rates of convergence can be observed: we prove that, when the negative part of the L\'evy measure exhibits an $\alpha$-stable density near the origin, with $1<\alpha<2$, the convergence rate is ruled by $\theta^{1/\alpha}|\ln \theta|^{1-\frac{1}{\alpha}}$, where $\theta$ is time until maturity.
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PDF链接：
https://arxiv.org/pdf/1105.0284