【摘要】：準(zhǔn)蒙特卡洛方法在計(jì)算金融,尤其是VAR模型等金融衍生品的定價(jià)和風(fēng)險(xiǎn)測(cè)量中正日益成為重要的數(shù)值分析工具；現(xiàn)在在一般的數(shù)學(xué)軟件及專業(yè)金融分析軟件中都可找到準(zhǔn)蒙特卡洛(low-discrepancy)序列的生成工具,便是其已具有相當(dāng)重要性的見證。過(guò)去二十年中,亦有大量研究人員憑借將此方法應(yīng)用到實(shí)際金融問題中所取得的出色成果而獲得專利。 本文中,我們將首先簡(jiǎn)要介紹金融衍生品及其相關(guān)的數(shù)值分析方法,綜述前人研究成果；然后,在正文分析中,從金融衍生品,VAR及靈敏度估計(jì)中引入準(zhǔn)蒙特卡洛方法的優(yōu)越性,接著對(duì)于多種將超均勻分布序列轉(zhuǎn)化為正態(tài)分布的方法進(jìn)行分析以得到估計(jì)的最佳精度。特別地,我們將討論一個(gè)最近的發(fā)現(xiàn)：對(duì)于超均勻分布序列,Box-Muller方法至少和逆變換方法一樣好。這是與眾多金融工程師和研究人員的默認(rèn)常識(shí)有悖的!我們基于Box-Muller方法的放射層次結(jié)構(gòu)假設(shè)了一個(gè)替代算法,用以對(duì)正態(tài)隨機(jī)變量分類,這對(duì)于VAR估計(jì)同樣是有效的。再次,我們還將運(yùn)用準(zhǔn)蒙特卡洛方法對(duì)歐式和亞式看漲期權(quán)的定價(jià)作誤差分析,并從結(jié)論說(shuō)明此方法的可行性；最后,我們將總結(jié)本文的成果,并對(duì)接下來(lái)進(jìn)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.
【學(xué)位授予單位】：山東大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：F830;F224

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本文編號(hào)：2192909