英文标题：
《Asymptotics for the Discrete-Time Average of the Geometric Brownian
Motion and Asian Options》
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作者：
Dan Pirjol, Lingjiong Zhu
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最新提交年份：
2017
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英文摘要：
The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps. We derive almost sure limit, fluctuations, large deviations, and also the asymptotics of the moment generating function of the average. Based on these results, we derive the asymptotics for the price of Asian options with discrete-time averaging in the Black-Scholes model, with both fixed and floating strike.
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中文摘要：
几何布朗运动的时间平均在数学金融中的亚式期权定价中起着至关重要的作用。在本文中，我们考虑了在大量平均时间步长的限制下，等距时间上采样的几何布朗运动的离散时间平均的渐近性。我们推导了几乎确定极限、涨落、大偏差以及平均值的矩母函数的渐近性。基于这些结果，我们推导了在Black-Scholes模型中，具有固定和浮动行使的离散时间平均亚式期权价格的渐近性。
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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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