延期算术平均亚式期权价格的一个近似封闭公式

延期算术平均亚式期权价格的一个近似封闭公式

张东¹, 鹿长余², 安玉娥³

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

收稿日期:2007-09-24 修回日期:1900-01-01 出版日期:2008-05-26 发布日期:2008-05-26
通讯作者: 鹿长余

An Approximate Closeform Formula of Deferred Arithmetic Average Asian Options

ZHANG Dong¹, LU Changyu², AN Yu e³

1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;2. Financial Research Center, Shanghai Finance University, Shanghai 201209, China;3. College of Sciences, Shanghai University, Shanghai 200466, China

Received:2007-09-24 Revised:1900-01-01 Online:2008-05-26 Published:2008-05-26
Contact: LU Changyu

摘要/Abstract

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.

关键词: 期权定价, 亚式期权, 延期, 风险中性, BlackScholes模型

Abstract: 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. Takinginto 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.

Key words: option pricing, asian options, deferred, risk neutral, BlackScholes model

中图分类号:

O242.2

张东, 鹿长余, 安玉娥. 延期算术平均亚式期权价格的一个近似封闭公式[J]. J4, 2008, 46(03): 443-447.

ZHANG Dong, LU Changyu, AN Yu e. An Approximate Closeform Formula of Deferred Arithmetic Average Asian Options[J]. J4, 2008, 46(03): 443-447.

[1]	曹桂兰, 佟昕叶. CEV跳-扩散模型下期权的定价[J]. 吉林大学学报(理学版), 2019, 57(1): 72-76.
[2]	甘小艇, 关南星, 张坤. 有限体积法定价带随机波动率的欧式期权[J]. 吉林大学学报(理学版), 2016, 54(06): 1307-1313.
[3]	袁缘, 张诚斌, 李辉来. 基于跳扩散过程的一类期权定价模型[J]. J4, 2013, 51(02): 187-190.