美式看涨期权的随机变量模型研究

发布时间：2018-04-11 20:58

本文选题：二叉树期权定价模型 + 维纳过程　；参考：《西安建筑科技大学》2012年硕士论文

【摘要】：在过去的30年，金融的衍生产品变得越来越重要。当今，随着我们的知识的增加，对金融产品理解的加深，期权交易在全球的诸多交易所都逐渐受欢迎。我们经常接触到的金融衍生产品之一就是期权，它的用途非常广泛，常常被用于公司的高层管理员的报酬、或者用于资本项目投资中、或是转移股票风险等等。投资者常常会关注长期的期权价格，而交易者则会关注短期的期权价格的变化。期权是一种选择权，它是股票交易双方之间签订的一份协议，，这份协议允许期权购买者在将来的某个特定日或这个日子之前，按照已经规定好的价格买卖一定数量的标的物品的权利，并且不承担任何义务。当买方决定执行期权合约时，卖方就必须卖出或买进合约中规定的标的物。市场具有动态性，所以我们对期权价格行为变化的正确理解是非常有必要的。本文主要介绍的是关于美式股票期权，而美式期权又有提前执行的情况，所以对于股票期权买方或卖方而言，如何判断最有利的时间点执行期权合约，使得投资者“风险最小化，利益最大化”成为我们讨论的焦点。本文首先介绍了期权的定义、分类、影响因素等，并且利用软件OP-EVAL4对股票期权进行定价，并且通过比较计算结果分析每种因素是如何影响股票期权价值的。然后简述已有的几种美式期权定价的数值方法，如：Black-Scholes期权定价模型、期权定价的二叉树定价模型、期权定价的三叉树定价模型、蒙特卡罗模拟法、有限差分法。已有的定价模型未考虑股息支付的情况，在此基础上，本文以美式看涨期权的定价问题为研究对象，引入了股票交易过程中存在的股息支付，根据随机误差校正的思想，结合美式看涨权的具体情况，考虑用lnS代替S来模拟股票价格，建立带有支付股息的新型二叉树期权定价模型。以美式看涨期权为例进行数据分析及检验，并且将计算结果与Black-Scholes期权定价模型的计算结果、不带股息支付的二叉树定价模型进行对比研究。
[Abstract]:Over the past 30 years, financial derivatives have become increasingly important.Today, as our knowledge grows and our understanding of financial products deepens, option trading is gaining popularity on many exchanges around the world.One of the financial derivatives we often come into contact with is option, which is used in a wide range of applications. It is often used in the remuneration of top executives of a company, or in capital account investments, or in transferring stock risks, etc.Investors tend to focus on long-term option prices, while traders focus on short-term price changes.An option is an option, an agreement between the two parties to a stock exchange that allows the buyer of an option to buy an option on or before a particular day in the future.The right to buy and sell a certain quantity of the subject matter at a specified price and without any obligation.When the buyer decides to execute the option contract, the seller must sell or buy the subject matter specified in the contract.The market is dynamic, so it is necessary to understand the change of option price behavior correctly.This article mainly introduces the American stock option, and American option has the situation of early execution, so for the buyer or seller of the stock option, how to judge the most favorable time point to execute the option contract,Make investor "risk minimization, profit maximization" become the focus of our discussion.This paper first introduces the definition, classification, influencing factors and so on of options, and makes use of software OP-EVAL4 to price stock options, and analyzes how each factor affects the value of stock options by comparing the results of calculation.Then several numerical methods of American option pricing are introduced, such as: Black-Scholes option pricing model, binomial tree pricing model, triple-tree pricing model, Monte Carlo simulation method and finite difference method.The existing pricing model does not take dividend payment into account. On this basis, the pricing problem of American call options is taken as the research object, and the dividend payment existing in the course of stock trading is introduced, according to the idea of random error correction.Considering the specific situation of American bullish power, we consider using lnS instead of S to simulate stock price and establish a new pricing model of binomial tree option with dividend payment.Taking American call option as an example, the data are analyzed and tested, and the results are compared with the results of Black-Scholes option pricing model and the binary tree pricing model without dividend payment.
【学位授予单位】：西安建筑科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.91

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