Adomian分解法在金融衍生品中的应用
本文涉及的期权有欧式期权、欧式期权(带红利)、亚式期权、房产期权. 首先文章推导出其偏微分方程, 创新地使用Adomian方法求出其近似解析解, 然后分析了部分参数对解的影响, 如得出无风险利率与期权是反相关, 波动率与期权也是反相关, 最后近似解析解做了误差分析, 结果是误差很小数量级最好的是 .
毕业论文关键词 期权定价; Adomian; 误差分析
Abstract
For Black - Scholes option pricing model, the main pricing method with binary tree method, finite difference method and monte carlo simulation, etc. The option pricing equation can be used to set the price of all kinds of financial derivatives, is an effective tool for various financial derivatives valuation. Its theory research is focused on how to construct new options to meet the demand of the market and how to option pricing. But its approximate analytical solution for the problem has always been a science.
This paper involves options have European option and European option (pidend), Asian options, housing options. First the article deduces the partial differential equation, the innovation to Adomian method is used to calculate the approximate analytical solution, and then analysis the influence of some parameters on the solution, such as the risk-free interest rate and options are related, volatility and options are related, the approximate analytical solution for the error analysis, the result is the best of the error is very small orders of magnitude is the .
Key words Option pricing; Adomian; error analysis
目 录
一．引言 5
1.1 研究背景 5
1.2 研究意义 5
1.3 国内研究现状与发展趋势 6
1.4 本文主要结构 6
1.5 符号含义 6
二．预备知识 7
2.1 期权定价的早期发展 7
2.2 Adomian方法 7
2.3 Black-Scholes期权定价理论 8
2.4 亚氏期权的定价理论 10
三．Adomian方法对欧式看涨期权的定价 12
3.1 终止条件转化为初始条件 12
3.2 Adomian迭代进行数值计算 13
3.3 误差分析 15
四．Adomian方法对带红利看涨期权的定价 17
4.1 终止条件转化为初始条件 17
4.2 Adomian迭代进行数值计算 18
4.3误差分析 20
五．Adomian方法对亚式期权的定价 22
5.1 终止条件转化为初始条件 22
5.2 Adomian迭代进行数值计算 23
5.3 误差分析 24
吹冰．房产期权 26
6.1一类具有违约风险的房产期权 26
6.2房产期权的微分方程 27
6.3 Adomian迭代进行数值计算 27
6.4 房产期权价格与初始时刻房价的关系 28
6.5不同 房产期权价格与初始时刻房价的关系的比较 28
七．结束语 30
7.1总结 30
7.2前景展望 30
八．致谢 31
参考文献 32
一．引言
1.1 研究背景