为欧亚和储亚期权简单、快速、准确定价的新方法

发布时间：2018-04-20 06:38

本文选题：近似算法 + 随机算法　；参考：《华中师范大学》2013年硕士论文

【摘要】：随着全球经济一体化和金融市场的飞速发展,金融领域衍生产品越来越多,也变得越来越重要,金融衍生产品又称金融衍生证券或金融衍生工具,它的价值依赖于其他更基本的标的变量。在当前国际金融市场上,期权是人们广泛使用的一种金融工具,也是人们较为熟知的衍生产品,世界上许多交易所的期权交易进行的非常活跃。期权按执行时间方式可分为欧式和美式期权,美式期权的持有者可以在期权有效期内任何时间行使权力,欧式期权只能在到期日执行。期权赋予持有者做某件事的权利,持有者不一定必须行使该权利。在对金融衍生品的研究中,期权定价理论是现代金融学基础之一,也是金融应用领域数学上最为复杂的问题,期权定价的模型与方法也是最重要、应用最广泛、难度最大的一种。股票期权价格是以所对应的标的股票价格为基础的,受股票价格的波动率及无风险收益率等参数的影响。目前关于期权定价方法研究的主要成果有：(1)Black-Scholes期权定价方法,(2)二叉树期权定价方法,(3)蒙特卡罗模拟方法,(4)有限差分法,(5)ε-套利定价方法,(6)区间定价法等。文中首先介绍了AMO算法,分析了该算法的误差范围和时间复杂度,同时列举了Akcoglu和Dai等其他学者对AMO算法改进后的分析结果。随后提出了一个为欧亚期权定价的准确有效的随机近似算法,该算法是AMO近似算法的改进,它从理论和实践上都提高了为欧亚期权定价的准确性,并给出了具体的数据和实证分析程序。本文提出的这个算法也可用来为储亚期权定价,该期权结合了欧亚期权和美亚期权的优点,是一种新兴期权。
[Abstract]:With the rapid development of global economic integration and financial market, more and more derivative products in the financial field are becoming more and more important. Financial derivatives are also called financial derivative securities or financial derivatives. Its value depends on other more basic underlying variables. In the current international financial market, option is widely used as a financial instrument, and it is also known as a derivative product. Many exchanges in the world are very active in option trading. The option can be divided into European option and American option according to the execution time. The holder of American option can exercise its power at any time during the period of validity of the option, and the European option can only be executed on the expiration date. Options give the holder the right to do something, and the holder does not have to exercise that right. In the research of financial derivatives, option pricing theory is one of the foundations of modern finance, and it is also the most complicated problem in the field of financial application. The model and method of option pricing are also the most important and widely used. The most difficult one. The stock option price is based on the corresponding underlying stock price, which is influenced by the volatility of the stock price and the risk-free rate of return. At present, the main achievements of the research on option pricing methods are as follows: 1 / 1 Black-Scholes option pricing method, 2) binomial tree option pricing method, 3) Monte-Carlo simulation method, 5) 蔚-arbitrage pricing method, and so on. This paper first introduces the AMO algorithm, analyzes the error range and time complexity of the algorithm, and lists the results of the improved AMO algorithm by other scholars such as Akcoglu and Dai. Then, an accurate and effective stochastic approximation algorithm for Eurasian option pricing is proposed, which is an improvement of AMO approximation algorithm. It improves the accuracy of Eurasian option pricing theoretically and practically. The specific data and empirical analysis program are also given. The algorithm proposed in this paper can also be used to price Asian reserve options, which combines the advantages of Eurasian options and American Asian options, and is a new option.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.91;F224

【共引文献】