延期算术平均亚式期权价格的一个近似封闭公式  

An Approximate Close-form Formula of Deferred Arithmetic Average Asian Options

作　　者：张东[1] 鹿长余[2] 安玉娥[3] 

机构地区：[1]上海理工大学理学院,上海200093 [2]上海金融学院金融研究中心,上海201209 [3]上海大学理学院,上海200466

出　　处：《吉林大学学报（理学版）》2008年第3期443-447,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10471043);上海高校选拔培养优秀青年教师科研专项基金(批准号:563802)

摘　　要：在标的价格服从几何布朗运动、收益服从对数正态分布的前提下,通过风险中性定价原理,对到期损益中的随机积分进行任意次Taylor近似,并由级数定义将此连续问题离散化,给出了延期算术平均亚式期权封闭形式的解析定价公式,并与Monte Carlo模拟得到的价格作为标尺对得到的公式进行精确性检验,结果表明,所得公式可以应用到金融实务中对此类衍生品定价中.It was supposed that the dynamic moving process of the stock price and the return was driven by Geometry Brownian Motion and the lognormal distribution respectively. Taking into account the risk-neutral environment, we got a closed-form analytical formula for deferred arithmetic asian options by the method of Taylor expansion of the stochastic integral formula within the terminal payoff. Furthermore, with the series definition of the definite integral, we transferred the continuous problem into a discrete one which is simple enough to figure out. Meanwhile we tested the accuracy of the formula with the Monte Carlo simulation as a benchmark and the result shows that the formula can be utilized to price the related financial derivatives.

关 键 词：期权定价 亚式期权 延期 风险中性 BLACK-SCHOLES模型 

分 类 号：O242.2[理学—计算数学]