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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (2): 185-196.doi: 10.3969/j.issn.1005-3085.2015.02.003

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Monte Carlo方法的精度分析及其在算术平均亚洲期权定价中的应用

张应应,  代春兰   

  1. 重庆大学数学与统计学院，重庆  401331
  • 收稿日期:2013-04-07 接受日期:2014-09-30 出版日期:2015-04-15 发布日期:2015-06-15
  • 基金资助:
    中央高校基本科研业务费项目 (CDJRC10100010; CQDXWL-2012-004).

Accuracy Analysis of Monte Carlo Method and its Application in the Arithmetic Average Asian Option Pricing

ZHANG Ying-ying,   DAI Chun-lan   

  1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331
  • Received:2013-04-07 Accepted:2014-09-30 Online:2015-04-15 Published:2015-06-15
  • Supported by:
    The Fundamental Research Funds for the Central Universities (CDJRC10100010; CQDXWL-2012-004).

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摘要： 本文讨论了Monte Carlo(MC)方法的精度分析及其在算术平均亚洲期权定价中的应用．首先，我们对MC方法的精度做了分析，讨论了两种依分布收敛到标准正态分布的情况(即对样本均值用标准差和标准误差进行标准化)．接下来对于三种MC方法(即Crude MC、Antithetic MC和Control MC)的精度及标准(误)差做了进一步的分析．然后，再介绍了MC方法在计算亚洲期权价格中的应用．最后，由算术平均亚洲看涨期权价格的数值模拟结果得到如下结论：两种模拟成功的频率都接近于理论概率；在对样本均值进行标准化为标准正态分布时，用标准差比用标准误差更好．

关键词: Monte Carlo方法, 精度分析, 算术平均亚洲期权, 期权定价

Abstract:

This paper discusses the accuracy analysis of the Monte Carlo (MC) method and its application in the arithmetic average Asian option pricing. First of all, we analyze the accuracy of the MC method and discuss two kinds of convergence in distribution to the standard normal distribution (namely standardizing the sample mean with the standard deviation and the standard error). Furthermore, we discuss the accuracy and the standard deviation (error) of the three kinds of MC methods (namely Crude MC, Antithetic MC, and Control MC). Then, we introduce the application of the MC method in the calculation of Asian option price. Finally, the numerical simulations of the arithmetic average Asian call option price show the following results: the two simulated success frequencies are both close to the theoretical probabilities; when the sample mean is standardized to be the standard normal distribution, the standard deviation is better than the standard error.

Key words: Monte Carlo method, accuracy analysis, arithmetic average Asian option, option pricing

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