摘要翻译：
几何布朗运动的一个时间积分的分布不是很清楚。为了给一个亚式期权定价，并获得它对时间参数、执行价格和基础市场价格的依赖程度，必须有几何布朗运动的时间积分分布，而且还需要有一种方法来操纵它的分布。本文给出了亚式期权及其衍生品（{\it{delta,gamma,theta和vega}}）价格中关键量的积分形式。例如，对于任何$a>0$$\MathBB{E}[(A_T-A)^+]=T-A+a^{2}\MathBB{E}[(a+A_t)^{-1}\exp(\frac{2m_T}{a+A_t}-\frac{2}{a}）]$，其中$A_t=\int^T_0\exp(B_S-S/2)DS$和$M_T=\exp(B_T-T/2).$
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英文标题：
《The derivatives of Asian call option prices》
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作者：
Jungmin Choi and Kyounghee Kim
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最新提交年份：
2007
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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：
  The distribution of a time integral of geometric Brownian motion is not well understood. To price an Asian option and to obtain measures of its dependence on the parameters of time, strike price, and underlying market price, it is essential to have the distribution of time integral of geometric Brownian motion and it is also required to have a way to manipulate its distribution. We present integral forms for key quantities in the price of Asian option and its derivatives ({\it{delta, gamma,theta, and vega}}). For example for any $a>0$ $\mathbb{E} [ (A_t -a)^+] = t -a + a^{2} \mathbb{E} [ (a+A_t)^{-1} \exp (\frac{2M_t}{a+ A_t} - \frac{2}{a}) ]$, where $A_t = \int^t_0 \exp (B_s -s/2) ds$ and $M_t =\exp (B_t -t/2).$
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PDF链接：
https://arxiv.org/pdf/0712.1093