股票价格的期权定价模型

论文总字数：13590字

目 录

摘要 1

第一章 课题背景与相关理论 3

1.1 课题背景与意义 3

1.2 早期模型 3

1.2.1 期权的含义 3

1.2.2 期权定价模型的发展 3

1.3 研究框架 4

第二章 现代期权定价模型 5

2.1 Black-Scholes模型 5

2.2 二项式定价法 7

2.2.1 单期二项式期权模型 7

2.2.2 n期看涨期权的二项式期权定价公式 9

2.3 Monte-Carlo模拟方法 10

第三章 股票期权的定价方法 12

3.1 股票的期权定价方法 12

3.1.1 权益资本的期权特征 12

3.1.2 期权定价模型 13

3.1.3 模型参数的估计 14

3.2 股票的期权定价实例 14

3.3 与蒙特卡洛模拟的对比 16

第四章 反思与展望 19

参考文献 20

股票价格的期权定价模型

李啸宇

（, China

Abstract: After 2000, the securities and exchange get good development. The resulting option, related investment consumption situation began to get the attention of experts and scholars in our country. Effective and scientific analysis is the efficient and the important way to avoid the risk, and it is the heart of normal operation and long-term development of the financial derivative securities.

The analysis of option pricing is mainly carried out in a large number of derivative securities pricing models, because:

(1) Option pricing is simple and easy.

(2) A number of options contracts can be built into a new portfolio, which can be more easily priced through the pricing of options.

(3) For all kinds of securities, the pricing principle is the one that changes from one to another. Therefore, by studying the pricing of options, it is possible to find the general conclusion of securities pricing.

In this paper, the number of option pricing problem is studied, trying to get some practical mathematical conclusion, and be able to show the dialectical relationship between mathematics and finance: on the one hand, mathematics is a powerful tool of financial research, on the other hand, the financial practice to promote the development of mathematics itself.

The thesis is divided into three chapters: the first chapter describes the development of option pricing theory, and we will introduce the concept of options, and brief the development of the option pricing model. The second chapter is about the modern option pricing model, in this chapter we will come into contact with three options pricing model, including the Black-Scholes model and the Monte Carlo simulation method and binomial pricing method. Understanding the three option pricing method is the foundation of the follow-up work. The third chapter describes the stock pricing method by option, it is the center of this article content. In this chapter, we will put the Black-Scholes model into the stock pricing method, it is also the innovation of this article. At the same time, with a kind of traditional stock pricing method, by contrast, expounds its feasibility. The fourth chapter is the summary of the thesis, and also the reflection and prospect of the author's work.

Keywords: Stock ; Option pricing ; Portfolio

第一章 课题背景与相关理论

1.1 课题背景与意义

改革开放使得在中国大陆上沉寂了20年之久的证券市场重新崛起，随着90年代上海交易所与深圳交易所的成立以及邓小平同志的南巡，中国股市开始迅速扩张，这是中国金融市场新的开始。然而,随着金融行业的不断扩张，金融事件如经济危机，泡沫经济等也都在给全球的经济带来难以估量的伤害。可以说，股价的合理性对国家的经济繁荣尤为重要，也牵扯到平民百姓的损益。这是本论文的出发点——希望借以分析股票的期权定价模型来探索股市的规律性。

1.2 早期模型

1.2.1 期权的含义

期权，简单地说就是一个订货合同，我们用一个例子来说明。

甲想在一年以后购得某品牌新上市的手机A，甲认为该手机新上市时会以8000元出售，超过了甲的承受范围，同时，有乙认为，该手机新上市时会以6000元出售，那么这时甲乙同意签署一份合同（即期权），并且甲付给乙期权费用，该合同规定，当手机上市时，甲有权利以7000元的价格从乙处购买手机A，但是甲不具备买入的义务。

这是最简单的期权模型，我们也可以规定将“买入”改为“卖出”，不变的只是支付期权费用的人是有权利而无义务的。

1.2.2 期权定价模型的发展

股市有风险，投资需谨慎。正是这种风险显示了期权的价格，长久以来，人们一直致力于研究如何用各种不确定因素估计标的资产的风险。

早在20世纪初，法国数学家路易斯在他的《投机理论》中就提出了对绝对的布朗运动的股票价格^[1]（股价的变动也是一个随机过程，其变化过程可以用布朗运动来模拟）的估值模型，站在买方的角度上进行统计，其期权价值主要是：

(1-1)

其中，S表示股价，X是执行价格，ι是与到期日的时间间隔，σ表示单位时间标准差。

,

因为该理论并未注意到正值货币的时间价值，投资者对风险的接受程度，所以该理论也只能作为定价模型的基石。

1964年，波内斯提出了在固定对数分布下的期权收益，给出了以下定价公式：

(1-2)

此处，表示股票预期收益率。

二十世纪中期，萨缪尔森寻找到欧式买方期权^[2]的定价方式，思考到需要具备较高预期收益率，此主要公式为：

(1-3)

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