二次有限体积法定价美式期权

doi:10.12286/jssx.2015.1.67

计算数学 ›› 2015, Vol. 37 ›› Issue (1): 67-82.DOI: 10.12286/jssx.2015.1.67

二次有限体积法定价美式期权

甘小艇^1,2, 殷俊锋¹

1. 同济大学数学系, 上海 200092;
2. 楚雄师范学院数学与统计学院, 云南楚雄 675000

收稿日期:2014-03-04 出版日期:2015-02-15 发布日期:2015-03-10
基金资助:
国家自然科学基金(11271289),云南省应用基础研究计划青年项目(2013FD045).

PDF ( 1188 ) 引用被引次数 ( 10 | 6 )

甘小艇, 殷俊锋. 二次有限体积法定价美式期权[J]. 计算数学, 2015, 37(1): 67-82.

Gan Xiaoting, Yin Junfeng. QUADRATIC FINITE VOLUME METHOD FOR PRICING AMERICAN OPTION[J]. Mathematica Numerica Sinica, 2015, 37(1): 67-82.

QUADRATIC FINITE VOLUME METHOD FOR PRICING AMERICAN OPTION

Gan Xiaoting^1,2, Yin Junfeng¹

1. Department of Mathematics, Tongji University, Shanghai 200092, China;
2. College of Mathematics and Statistics, Chuxiong Normal University, Chuxiong 675000, Yunnan, China

Received:2014-03-04 Online:2015-02-15 Published:2015-03-10

本文考虑二次有限体积法定价美式期权.构造了隐式欧拉和Crank-Nicolson两种全离散二次有限体积格式,并得到相应的线性互补问题.采用基于超松弛迭代的模方法求解线性互补问题,并与投影超松弛迭代法作数值比较.数值实验结果表明Crank-Nicolson二次有限体积格式的求解效率高于隐式欧拉格式,模方法的求解速度较快,二次有限体积法的求解精度较高.

关键词： 二次有限体积法, 美式期权, 模方法, 投影超松弛迭代, 线性互补问题

Quadratic finite volume method for pricing American options is studied. The implicit-Euler and Crank-Nicolson quadratic finite volume schemes are proposed, and the modulus-based successive overrelaxation methods are applied to solve the linear complementarity problems. Numerical experiments show that quadratic finite volume method based on Crank-Nicolson scheme is much efficient, and the modulus-based successive overrelaxation method is faster than the projected successive overrelaxation method.

Key words: quadratic finite volume method, American option, modulus methods, projected successive overrelaxation, linear complementarity problems

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摘要

二次有限体积法定价美式期权

QUADRATIC FINITE VOLUME METHOD FOR PRICING AMERICAN OPTION

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