美式期权定价的改进的奇点分离法

发布时间：2018-01-05 20:06

本文关键词：美式期权定价的改进的奇点分离法　出处：《西南财经大学》2014年硕士论文　论文类型：学位论文

【摘要】：美式期权的定价问题一直是热点,由于它的解析解很难得出,因此,众多学者都热衷于寻找一种既有效又精确的数值方法来求解美式期权。美式期权定价问题可以表示成一个热方程的自由边界问题,而这种转换也产生了许多不同的数值方法。在本文中,我们将介绍一种有限差分数值算法来求解美式期权价格。因为美式期权和欧式期权都满足BS方程,它们的差也满足转换后的BS方程,根据这一特性,已经有学者研究出奇点分离法,使得初始边界条件为零,消除了奇点影响。奇点分离法计算的结果比较精确,然而还是有不足之处,因为它跟常有的数值计算方法一样,确定计算域时都会取一个足够大的值来保证足够小的截断误差,然而这种做法使得许多格点上的计算值都是多余的。有学者就根据BS偏微分方程的性质制造人工边界来避免无谓的计算过程。本文中介绍的方法将在奇点分离法的基础上,引入人工边界条件,计算的结果也表明结合的方法比奇点分离法要精确。其中为了得到精确解来作为对比,我们采用二叉树的计算结果作为参考。
[Abstract]:The pricing of American option has always been a hot topic, because its analytical solution is very difficult to come out, so. Many scholars are keen to find an effective and accurate numerical method to solve American option. The American option pricing problem can be expressed as a free boundary problem of heat equation. This conversion also produces many different numerical methods. In this paper, we will introduce a finite difference numerical algorithm to solve the American option price, because both American option and European option satisfy BS equation, their difference is also satisfied with the converted BS equation. According to this characteristic, some scholars have studied the singularity separation method, which makes the initial boundary condition zero and eliminates the singularity effect. The results of the singularity separation method are more accurate, but there are still some shortcomings. Because it takes a large enough value to ensure a small truncation error when determining the computational domain, as is often the case with numerical methods. However, this method makes the calculation values on many lattice points superfluous. Some scholars have made artificial boundaries according to the properties of BS partial differential equations to avoid the unnecessary calculation process. The method introduced in this paper will introduce artificial boundary conditions on the basis of the singular point separation method. The results of calculation also show that the combined method is more accurate than the singular point separation method. We use the result of binary tree as a reference.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.91

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