金融衍生品的Monte Carlo模拟算法及VAR估计算法的改进
发布时间：2018-08-20 07:41
【摘要】：准蒙特卡洛方法在计算金融,尤其是VAR模型等金融衍生品的定价和风险测量中正日益成为重要的数值分析工具；现在在一般的数学软件及专业金融分析软件中都可找到准蒙特卡洛(low-discrepancy)序列的生成工具,便是其已具有相当重要性的见证。过去二十年中,亦有大量研究人员凭借将此方法应用到实际金融问题中所取得的出色成果而获得专利。 本文中,我们将首先简要介绍金融衍生品及其相关的数值分析方法,综述前人研究成果；然后,在正文分析中,从金融衍生品,VAR及灵敏度估计中引入准蒙特卡洛方法的优越性,接着对于多种将超均匀分布序列转化为正态分布的方法进行分析以得到估计的最佳精度。特别地,我们将讨论一个最近的发现：对于超均匀分布序列,Box-Muller方法至少和逆变换方法一样好。这是与众多金融工程师和研究人员的默认常识有悖的!我们基于Box-Muller方法的放射层次结构假设了一个替代算法,用以对正态随机变量分类,这对于VAR估计同样是有效的。再次,我们还将运用准蒙特卡洛方法对欧式和亚式看涨期权的定价作误差分析,并从结论说明此方法的可行性；最后,我们将总结本文的成果,并对接下来进一步的研究方向做出展望。
[Abstract]:Quasi-Monte Carlo method is becoming an important numerical analysis tool in the calculation of finance, especially in the pricing and risk measurement of financial derivatives such as VAR model. The generation of quasi-Monte Carlo (low-discrepancy) sequences can now be found in both general mathematical software and professional financial analysis software, which is evidence of its importance. Over the past two decades, a large number of researchers have patented the method for its excellent results in practical financial problems. In this paper, we will first briefly introduce financial derivatives and their related numerical analysis methods, summarize the previous research results, and then introduce the advantages of quasi-Monte Carlo method from the financial derivatives VAR and sensitivity estimation in the text analysis. Then, several methods to transform the super-uniform distribution sequence into normal distribution are analyzed to obtain the best estimation accuracy. In particular, we will discuss a recent finding that the Box-Muller method is at least as good as the inverse transformation for super-uniform distribution sequences. This is contrary to the default common sense of many financial engineers and researchers! We assume an alternative algorithm for classifying normal random variables based on the radiation hierarchy of Box-Muller method, which is also valid for VAR estimation. Thirdly, we will use the quasi-Monte Carlo method to analyze the pricing error of European and Asian call options, and illustrate the feasibility of this method from the conclusion. Finally, we will summarize the results of this paper. The future research direction is prospected.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830;F224
本文编号：2192909
[Abstract]:Quasi-Monte Carlo method is becoming an important numerical analysis tool in the calculation of finance, especially in the pricing and risk measurement of financial derivatives such as VAR model. The generation of quasi-Monte Carlo (low-discrepancy) sequences can now be found in both general mathematical software and professional financial analysis software, which is evidence of its importance. Over the past two decades, a large number of researchers have patented the method for its excellent results in practical financial problems. In this paper, we will first briefly introduce financial derivatives and their related numerical analysis methods, summarize the previous research results, and then introduce the advantages of quasi-Monte Carlo method from the financial derivatives VAR and sensitivity estimation in the text analysis. Then, several methods to transform the super-uniform distribution sequence into normal distribution are analyzed to obtain the best estimation accuracy. In particular, we will discuss a recent finding that the Box-Muller method is at least as good as the inverse transformation for super-uniform distribution sequences. This is contrary to the default common sense of many financial engineers and researchers! We assume an alternative algorithm for classifying normal random variables based on the radiation hierarchy of Box-Muller method, which is also valid for VAR estimation. Thirdly, we will use the quasi-Monte Carlo method to analyze the pricing error of European and Asian call options, and illustrate the feasibility of this method from the conclusion. Finally, we will summarize the results of this paper. The future research direction is prospected.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830;F224
【参考文献】
相关期刊论文 前1条
1 吴飞;;产生随机数的几种方法及其应用[J];数值计算与计算机应用;2006年01期
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