The Pricing Of European Options With Transaction Costs By The Finite Element Method

In the present society, the financial industry is developing fast thus all kinds of financial derivatives exist. During the late decades, the financial derivatives also have great effect on our economy. Option—one of the most important financial derivative. The usual financial derivative we talked, is about one kind of right, this right let the owner sell or buy the target asset at some future time, with a confirmed value. What.s more, more and more people is focusing on knowing it because option have excellent risk prevention and value discover ability etc. Since option stands for the key tools of risk management and has above advantages, it is necessary for us to do further study of it. Predecessors have had done great study on option pricing theory, also build related formula of option pricing. Though we already have option pricing formula, but most people prefer to use numerical method. Normally, there have three types of most commonly used numerical method for option pricing, that is 1. Finite difference method, 2. Finite element method, 3. Binary tree method.This article is based on European option pricing model with transaction costs by Hoggord. Normally the European option pricing model would be a linear parabolic differential equation, but we here use transaction costs as a variable, thus European option pricing model become a nonlinear parabolic differential equation. In this article, we use finite element method, try to search some of its characters in numerical calculation aspect. We will give some examples of numerical calculation, use Matlab to programming, and get the graphic of equation. At last compare with financial theory and the results obtained by the finite difference method prove their results are the same.