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二次有限体积法定价美式期权
引用本文: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.
作者姓名:甘小艇  殷俊锋
作者单位: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
基金项目: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).
摘    要: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
收稿时间:2014-03-04;

QUADRATIC FINITE VOLUME METHOD FOR PRICING AMERICAN OPTION
Gan Xiaoting,Yin Junfeng.QUADRATIC FINITE VOLUME METHOD FOR PRICING AMERICAN OPTION[J].Mathematica Numerica Sinica,2015,37(1):67-82.
Authors:Gan Xiaoting  Yin Junfeng
Institution:1. Department of Mathematics, Tongji University, Shanghai 200092, China;
2. College of Mathematics and Statistics, Chuxiong Normal University, Chuxiong 675000, Yunnan, China
Abstract: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.
Keywords:quadratic finite volume method  American option  modulus methods  projected successive overrelaxation  linear complementarity problems
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