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摘要：随着中国资本市场的迅速发展和居民收入水平的提高, 越来越多的人参与到期权、股票等市场投资中, 希望能够实现财富的保值和增值. 虽然这一些投资可以给带来高回报, 但是它们还是具备较高的风险, 随着时刻的变化, 价格也在不断的发生改变, 投资者们急需一种理论来解释价格变化的原因, 并需要一种科学的预测方法来指导投资, 达到规避风险, 获得较高回报的结果. 本文主要讲述了期权定价的三种数值方法, 蒙特卡洛模拟法、二叉树法及有限差分法. 将他们的思想、基本原理、求解步骤进行说明, 并用MATLAB进行编程. 对于所编辑的程序都将进行计算. 在现今中国的市场中, 也有期权产品, 将这三中方法运用于现今中取宝山钢铁股份有限公司的数据进行计算, 观察结果, 总结得有限差分法更加适合于中国期权市场. 在对于期权进行分析后, 对于股票价格, 也可以进行预测, 提出蒙特卡洛-均值法混合预测. 蒙特卡洛-均值预测法综合了蒙特卡罗法与均值预测法的优点, 也避免了这两种方法的缺点. 股票价格预测过程中, 一般第一个数据较为精确, 且波动率偏小, 预测值更为精确.5328
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关键词： 蒙特卡洛模拟法；二叉树法；有限差分法；期权；均值预测法
Numerical Solution Algorithms and Stock Options Prediction Model
Abstract:With the rapid development of China's capital market and income levels increase, more and more people to participate in options, stocks and other investments in the market, hoping to achieve wealth preservation and appreciation, although some investment which can bring high returns to , but they still have a higher risk, with the change of time, prices have also been changed, investors need a theory to explain the reasons for price changes, and the need for a scientific prediction methods to guide investment, reach to avoid risk, to obtain higher returns results. this paper describes three kinds of numerical methods of option pricing, Monte Carlo simulation, the binary tree method and finite difference method. their ideology, basic principles for solving steps described and used MATLAB programming for the edited program will be calculated in the current Chinese market, there are also options products, these three methods used in today's Baoshan Iron & Steel Co., Ltd., is taken to calculate the data, observations, summed it up finite difference method is more suitable for Chinese options markets in an analysis of the options, the stock price, it can be predicted, proposed Monte Carlo - mean method hybrid prediction. Monte Carlo - mean prediction method combines the Monte Carlo method and mean prediction method has the advantage, but also to avoid the drawbacks of these two methods. stock price forecasting process, generally the first data is more accurate, and the volatility of smaller, more accurate predictions.
Keywords: Monte Carlo simulation method; binary method; finite difference method; options; mean prediction
目录
1. 引言 1
2. 预备知识 1
2.1. 蒙特卡罗法 1
2.1.1. 蒙特卡罗法的基本原理 1
2.1.2. 蒙特卡罗法的应用 3
2.2. 期权定价的二叉树法 5
2.2.1. 二叉树法的基本原理及计算步骤 6
2.2.2. 无收益资产的期权定价 8
2.3. 有限差分法 12
2.3.1. 有限差分法的基本思想 12
2.3.2. 差商法 13
2.3.3. 内含有限差分法和外推有限差分法 14
2.3.4. 期权的外推有限差分法定价 16
2.4. 本节小结 17
3. 期权定价的三种基本数值方法来求解宝钢期权并进行比较 18
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