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浙江大学学报（理学版）
浙江大学学报（理学版）  2017, Vol. 44 Issue (5): 542-547    DOI: 10.3785/j.issn.1008-9497.2017.05.008
数学与计算机科学     
基于方差缩减的高维美式期权Monte Carlo模拟定价
陈金飚, 林荣斐
台州学院 数学与信息工程学院, 浙江 台州 317000
A Monte Carlo simulation on pricing of high dimensional American options based on variance reduction
CHEN Jinbiao, LIN Rongfei
School of Mathematics & Information Engineering, Taizhou University, Taizhou 317000, Zhejiang Province, China
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摘要： 美式期权给予持有者在到期日之前任何时刻的权利，因涉及最佳执行时刻问题定价较为复杂. Monte Carlo方法其估计误差及收敛速度与问题的维数独立，可较好地处理高维衍生证券问题，且方法灵活易于实现.利用最小二乘蒙特卡洛方法（LSM），结合存储量减小技术与方差缩减技术，将 Monte Carlo 模拟方法应用于多标的资产的美式期权定价，并比较、分析了不同方差缩减技术的效果及适用范围.
关键词： Monte Carlo方法;  美式期权;  方差缩减技术;  定价    
Abstract: American options allow holders to execute an order at any moment before due date. However, the pricing of American options is comparatively complicated because it involves the optimal stopping rule. Monte Carlo method is flexible and easy to implement. Besides, its error estimation and convergence rate are independent of the dimension of the problem, providing Monte Carlo method a great advantage over classical numerical approaches in option pricing. This paper combines the Least Square Monte Carlo method with some variance reduction techniques and a memory reduction approach to price multi-asset American-style options, then compares the efficiency of different variance reduction techniques, and analyzes their application.
Key words: Monte Carlo method    American options    variance reduction techniques    pricing
收稿日期: 2017-01-16 出版日期: 2017-05-01
CLC:  O242.28  
基金资助: 浙江省教育厅一般科研项目（Y201431077）；浙江省教育厅高等学校访问学者教师专业发展项目（FX2016073）.
通讯作者: 林荣斐,ORCID:http://orcid.org/0000-0002-4347-0905,E-mail:linrfei@tzc.edu.cn.     E-mail: linrfei@tzc.edu.cn
作者简介: 陈金飚(1971-),ORCID:http://orcid.org/0000-0003-0339-5880,男,硕士,讲师,主要从事Monte Carlo模拟、数据分析、图像处理等研究.
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引用本文:

陈金飚, 林荣斐. 基于方差缩减的高维美式期权Monte Carlo模拟定价[J]. 浙江大学学报（理学版）, 2017, 44(5): 542-547.

CHEN Jinbiao, LIN Rongfei. A Monte Carlo simulation on pricing of high dimensional American options based on variance reduction. Journal of ZheJIang University(Science Edition), 2017, 44(5): 542-547.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.05.008    或    https://www.zjujournals.com/sci/CN/Y2017/V44/I5/542

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