Adomian分解法在期权定价中的应用
毕业论文关键字：Adomian方法，电力衍生品，欧式看涨期权
The application of Adomian decomposition method on option pricing
Abstract:The development of the economicsis linked closely with financial market,
while the option is one of the important areas of the market. In recent years, there are
a lot of researches whichhave been reported, but lots of them are about
arithmeticsolution. However, we mainly discussed approximate analytic solution of
the option price. According to the approximate analytic solution, we can conclude the
influence of parameters on the option price. We mainly use the Adomian
decomposition method to solve the problem of the option price. Here are two
examples.
The first one is about European Option. We use Adomian decomposition method to
solve the famous Black-Scholes equation. And when the order get to the 20-term, our
deviation is 0.00001 which is very close to 0. So the result prove that our method is
very effective and accurate.
The second one is about electricity derivatives. We use the same method to solve the
similar problem. And when the order get to the 10-term, our deviation is
1710 5 . 1
which is very small. The result also prove that our method is very excellent.
In conclusion, it is effective and worth popularizing when solving the approximate
analysis solutions of option pricing by Adomain decomposition method.
Key words:Adomian decomposition method, electricity derivatives, European Option.
目 录
一. 引言 2
1.1 概述 2
1.1.1 研究背景 .2
1.1.2 研究意义 3
1.1.3 国内外研究现状与发展趋势 .3
1.2 预备知识 .4
1.2.1 假设与符号 4
1.2.2 Adomian方法介绍 .4
二．Adomian分解法求欧式看涨期权的近似解析解 . .6
2.1 Black-Scholes期权定价理论 .6
2.1.1 Black-Scholes偏微分方程 .6
2.1.2 边界条件 8
2.2 初值条件 .8
2.3 Adomian迭代进行数值计算 9
2.4 数值拟合 10
2.5 误差分析 11
2.6 期权价格 13
三. Adomian方法对电力衍生品的定价 . 13
3.1 电力衍生品的概述 .13
3.1.1 背景知识 13
3.1.2 PJ模型概述 .14
3.2 初值条件 15
3.3 Adomian迭代进行数值计算 .15
3.4 数值拟合 .16
3.5 误差分析. 18
3.6 期权价格 19
四．基于多元回归与技术分析的组合股票价格预测. 20
4.1 背景概述 20
4.2 常用技术指标 20
4.3 回归预测模型及实例分析 .21
4.4 小结 22
五．总结. 23
5.1 小结 23
5.2 展望 23
致谢. 24