美式期权定价的数值方法比较研究

发布时间：2018-06-16 22:59

本文选题：美式期权 + 自由边界　；参考：《西安工程大学》2012年硕士论文

【摘要】：期权定价理论是当前金融数学和金融工程学科研究和讨论的前沿和热点问题之一．美式期权相比欧式期权具有可提前执行的特权，这导致了其定价问题难度大大增加．本文从提前执行策略、最优执行边界、期权性质等方面剖析了美式期权的价格构成原理，重点解决如何利用数值计算方法求解期权价格以及方法的实现．主要研究内容如下：第1章系统介绍了有关金融衍生产品定价的基本概念，发展历史及研究现状，同时阐述了研究美式期权定价的理论和实际意义．第2章完整的给出了Black-Scholes模型，并借鉴类似的方法分别推导出了美式期权定价模型，有交易成本和红利的欧式美式期权定价模型．第3章主要给出了几种常用美式期权定价的数值计算方法：如树图方法，，有限差分法和有限元法．并借用程序设计的思路给出了详细的计算过程和步骤．第4章以数值算例为研究内容，利用MATLAB软件进行数值试验，并从收敛性、收敛速度、计算精度及稳定性等角度分析实验所得结果．最后，以真实的股票价格为研究对象，讨论了随机波动率条件之下的美式期权定价问题，并利用时间序列中的有关方法，采用真实数据做波动率预测，用数值方法求出了股票期权的价格．第5章分析汇总并给出了进一步研究的问题．
[Abstract]:Option pricing theory is one of the frontier and hot issues in the research and discussion of financial mathematics and financial engineering. Compared with European option, American option has the privilege to execute ahead of time. This leads to a great increase in the difficulty of pricing problems. This paper analyzes the pricing principle of American options from the aspects of early execution strategy, optimal execution boundary, option nature, and so on. The main contents of this paper are as follows: chapter 1 systematically introduces the basic concepts of pricing of financial derivatives. In chapter 2, the Black-Scholes model is given, and the American option pricing model is derived by using similar methods. European American option pricing model with transaction costs and dividends. Chapter 3 mainly gives several numerical calculation methods of American option pricing in common use, such as tree graph method, The finite difference method and finite element method are used to give the detailed calculation process and procedure. Chapter 4 takes numerical example as the research content, carries on the numerical experiment with MATLAB software, and from the convergence, the convergence speed, Finally, taking the real stock price as the research object, the problem of American option pricing under the condition of random volatility is discussed, and the relevant methods in time series are used. The real data is used to predict volatility and the price of stock options is calculated by numerical method.
【学位授予单位】：西安工程大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.91;O241.82

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