摘要翻译：
当股票价格过程$S$服从一般鞅时，我们研究了在价看涨期权价格的小时间渐近性中的先导项。这相当于研究$s$的第一居中绝对矩。我们证明了如果$S$具有连续部分，则超前项在时间上为$\sqrt{T}$，并且只依赖于波动率的初始值。此外，该项在$T$中是线性的当且仅当$S$是有限变差的。无穷变分纯跳过程的导项介于这两种情况之间；我们得到了它们对类稳定小跳跃的精确形式。为了得到这些结果，我们使用了$S$的自然近似，因此只需要对L\'Evy过程类进行计算。
---
英文标题：
《Small-Time Asymptotics of Option Prices and First Absolute Moments》
---
作者：
Johannes Muhle-Karbe, Marcel Nutz
---
最新提交年份：
2011
---
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
--
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
--

---
英文摘要：
  We study the leading term in the small-time asymptotics of at-the-money call option prices when the stock price process $S$ follows a general martingale. This is equivalent to studying the first centered absolute moment of $S$. We show that if $S$ has a continuous part, the leading term is of order $\sqrt{T}$ in time $T$ and depends only on the initial value of the volatility. Furthermore, the term is linear in $T$ if and only if $S$ is of finite variation. The leading terms for pure-jump processes with infinite variation are between these two cases; we obtain their exact form for stable-like small jumps. To derive these results, we use a natural approximation of $S$ so that calculations are necessary only for the class of L\'evy processes.
---
PDF链接：
https://arxiv.org/pdf/1006.2294