美式期权定价的一种蒙特卡洛方法

A Monte-Carlo Method for Pricing American Options

期权定价理论是目前金融工程、金融数学等领域所研究的前沿和热点问题,基于此,本研究中,使用蒙特卡洛方法解决美式期权定价问题。首先,简要介绍期权的相关概念和分类、美式期权的基本知识;然后,提出合理的假设,根据美式期权的行权特点建立相应的数学模型,推导得出美式期权价格的数学期望表达式,再根据表达式设计一种蒙特卡洛方法进行计算;最后,得出在合理假设条件下美式看涨期权和美式看跌期权的价格计算方法。假设利用传统的有限差分法得出的美式看涨期权和美式看跌期权价格的数值结果是"准确解",然后将蒙特卡洛方法得到的数值结果与用有限差分法得到的准确解进行比较,并进一步讨论蒙特卡洛方法的优越性及其推广。

Option pricing is now a hot topic in financial engineering and mathematical finance,In this project, we develop a Monte-Carlo method for pricing American options.Firstly, we will introduce some basic conception regarding to Options and the classification of them, and then ,we introduce American options.Secondly ,we put forward several assumptions, and basing on the characteristics of American options,we establish a mathematical model to calculate the price of American options.Finally we design a Monte-Carlo method to solve the model and get numerical results.We suppose that the numericalresults from the finite difference method are ＂exact＂, and compare these exact solutions with those obtained from the Monte-Carlo method.Finally,we will discuss the advantages of Monte-Carlo method and how to extend the use of it.