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这篇论文的主要问题是如何重视美国的选择。选项值是唯一已知的选择是行使时,到期或不到期。当老板决定行使期权或是选择成熟时间,可以确定的价格选择停止将交换资产的所有者的条件做为有利的选择。当一个购买股票,她不知道将基础资产的未来价格,我们假设它是一个随机过程,很难在合同价格并且不知道会改变价格。这种非线性特性的选项,这样可以让用户计算代价合同一个挑战性的过程,大量的金融研究的焦点和出版物中都有提到。

American options are financial derivatives, an instrument whose value is derived from an underlying asset, usually a stock. Black and Scholes (1973) described an option as: 'a security giving the right to buy or sell an asset, subject to certain conditions, within a specified period of time'.

The main question of this dissertation is how American options can be valued. The option value is only known with certainty when the option is exercised, either at maturity or not. When the owner decides to exercise the option or it is the option maturity time, it is possible to determine the price of the option as the strike will be exchanged by the asset in the case that the conditions are favourable for the owner of the option. When the one buys the option, she does not know what will be the future price of the underlying asset, and assuming it follows a random process it is hard to put a price on such contract without knowing what will be the price change. This non linear feature of the option makes calculating the price to pay for such contracts a challenging process and has been the focus of a large number of financial studies and publications.

This dissertation deals with the most popular methods for pricing American options and their implementation in MatLab®, including a graphic user interface.

The methods studied include the Black and Scholes (1973) European option pricing as the starting point, followed by the Barone Adesi and Whaley (1987) analytical approximation. Then the binomial and trinomial lattice methods presented in Cox, Ross and Rubinstein (1979) are considered also as the Finite difference approximations models AAA. The most sophisticated method is the Least Squares Monte Carlo simulation presented in Longstaff and Schwartz (2001).

The analysis of the different option pricing methods in this dissertation follow most of the assumptions made by Black and Scholes (1973), the short term interest rate and the dividend are assumed to be known and constant, the underlying stock follows a log normal distributed geometric Brownian motion, the markets are frictionless and finally it exists the possibility of forming a riskless portfolio, consisting of the option and underlying stock.

The dissertation is organised as follows: a brief literature survey is provided in the next Chapter. The analytical approximation method and the numerical methods used are described on Chapter 3 and their implementation in Matlab environment is given in chapter 4. Numerical results are given in Chapter 5. The conclusion and future developments are presented in Chapter 6.

Chapter 2 provides a survey of some of the most relevant publications in American Option Pricing, with focus on analytical approximations, lattice and finite difference methods, more precisely, binomial and trinomial trees, explicit, implicit and Crank本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。