障碍期权的定价与复制
本文将单边障碍期权纳入研究范畴，利用鞅以及概率论的知识得到完整单边欧式障碍期权的理论公式。此外，在动态复制过程中给障碍加入了一个附加值,使得在动态基础上的复制成本要比原来更低。最后，在标的价格未触及障碍值前，我还通过将其收益由零值改为一个固定金额，从而得出了一种新型障碍期权，命名为标准障碍期权并通过图表形式证明其有效性, 并以SHFE铜作为标的物，对理论公式，动态复制和技巧调整后的三个期权价加以对比，可知调整后的动态定价更符合风险不断波动的中国市场。36842
毕业论文关键词： 鞅；伊藤原理；动态复制；风险中性定价；障碍期权
The Pricing and Replication of Barrier Options
Abstract: The prevalence of barrier options has brought remarkable influence to scientists and researchers throughout all over the world. And it is favored by market. The pricing of Barrier options is one of the most important questions in financial statistics.
In this paper, we focus on the single barrier options. First, we get the theoretical pricing formula of general barrier option based on concepts, contents and methods of options, the martingale and probability. Besides, reducing the option price of dynamic replication can be abstained by giving an add value on the barrier value. Last, we set a fixed value on the payoff in an interval at the maturity date without hitting either the lower or the upper boundaries to give the explicit barrier options being called stand and barrier options, and get further to verify the validity Appling the analysis of graph. Then we conclude that adjusted dynamic pricing method will be more suitable for the Chinese condition in stock market in the way of comparing the consequences among the static one, the dynamic one and the adjusted one for SHGE copper.
Keywords: martingale; Ito theory; Dynamic replication; risk-neutral valuation; barrier option
目录
摘要 ii
Abstract iii
目录 iv
1 绪论 1
1.1 期权的概述 1
1.2 障碍期权研究历史发展 2
1.3 本文工作及其意义 2
2 预备知识 4
2.1 股价变化过程及ITO定理 4
2.1.1 文纳过程 4
2.1.2 Itô过程 5
2.1.3 Itô定理 7
2.2 基础概率理论 8
2.3 风险中性假设 9
3 鞅与概率分配理论 11
3.1 鞅测度 11
3.2 随机过程与概率分配 15
3.2.1 布朗运动及其极大极小值的概率分布 15
3.2.2 含有漂浮项布朗运动及其极大值的联合概率分布 20
3.2.3 几何布朗运动及其极大极小值的联合概率分布 23
3.2.4 标的价格及其极大极小值的联合概率分布 25
4 障碍期权的理论定价 28
4.1 普通欧式期权 28
4.2 单边障碍期权定价及DELTA动态复制 29
5 新型障碍期权及实证分析 36
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