## Black-Scholes方程的求解方法分析及应用

关键词  期权定价; 布莱克—斯科尔斯模型; 同伦摄动方法; 蒙特卡罗
Abstract
Option pricing theory is one of the most important results of modern financial theory. Option pricing equation can be used to formulate all kinds of financial derivative products. It is an effective tool to all kinds of financial derivatives valuations. Due to their outstanding contribution to option pricing theory, Scholes and Merton has won the 1997 Nobel Prize in Economics. Their theoretical research focuses on how to construct a new option to meet the needs of the market and how to price the option .
For the Black-Scholes' option pricing model, the main pricing methods include partial differential equations, approximate analytic solution, binary method, finite difference method and Monte Carlo simulation, etc. The paper derivates the accurate analytical solution to partial differential equations that innovate to use the homotopy perturbation method to sovle the approximate analytical solution and uses Monte Carlo simulation method to forecast China's stock market price.

Key words  Option pricing; Black-Scholes; Homotopy Perturbation Method; Monte Carlo
目录

1. 1 研究背景    1
1. 2 研究意义    2
1. 3 期权定价理论的近期发展    2
1. 4 本文主要结构    4
1. 5 假设与符号    5

2. 1 期权定价的早期发展    6
2. 2 股票价格的行为模拟    9
2. 3 Black-Scholes期权定价理论    12
2. 4 期权定价的应用    16

3. 1 同伦摄动方法的基本原理    18
3. 2 同伦摄动方法求解Black-Scholes方程    19
3. 3 B-S的解与HPM求出的近似解比较    20

4. 1 蒙特卡罗方法概述    23
4. 2 蒙特卡罗的基本概念,原理    23
4. 3 蒙特卡罗模型建立    24
4. 4 应用领域    24

5. 1 总结    26
5. 2 前景展望    26

1. 1 研究背景

------分隔线----------------------------