美式期权定价的指数型差分格式分析

金融衍生物就是一种风险管理的工具,期权是最重要的金融衍生工具之一,它在防范和规避风险以及投机中起着非常重要的作用,期权理论的核心就是期权定价问题.由于美式期权与欧式期权不同,它不可能得到解的显式表达式,所以研究它的数值解以及解本身的一些性质就显得尤为重要.基于Black-Scholes微分方程,对美式期权的指数型差分格式进行推导,结果表明,用指数型差分格式可以得到有效的数值解.

On Exponential Difference Method of American Option Pricing

Financial derivative is a risk management tool .Option is one of the most important derivatives . It is in prevent and avoid the risks and speculation plays a very important role .Option pricing is the core of the option theory .American option is different from European one .For American option ,noanalytic for-mula and exact solution can be obtained .Thus ,it's very important to discuss various numerical methods for American option .In this dissertation ,the exponential difference scheme for American option pricing has been developed on the base of Black and Scholes equation .Numerical examples show the convergence and efficiency of our algorithm .