基于主成份分析思想的金融衍生证券定价伪蒙特卡罗模拟改进技术

Quasi-Monte Carlo Method for Financial Derivatives Securities Based on Principal Component Analysis

在伪蒙特卡罗模拟应用于金融衍生证券定价过程中,标准维纳过程的构造方法对模拟估计的效果具有十分重要的影响。本文首先对现有的传统标准维纳过程构造和布朗桥构造方法进行简要分析;在此基础上,基于主成份分析基本思想,对能够用于有效减少实际问题维数的主成份构造方法及其在高维衍生证券定价问题中的应用进行了深入研究探讨,为进一步改进蒙特卡罗模拟在金融衍生证券定价中的应用效果提供有效途径。

Methods for constructing standard Winner Process can have a very important influence on estimation result of Monte Carlo simulation in the course of pricing financial derivative securities. This paper makes a brief analysis for existing constructing methods such as traditional standard Winner Process and Brownian-Bridge. Then, basing on fundamental idea of principal component analysis, we carry a deep research and exploration for principal component constructing method, which may be used to reduce effective dimensions of solved problem, and its application in pricing high-dimension derivative securities. Lastly, this paper gives an effective way to improve simulation result of Monte Carlo methods in pricing high-dimension derivative securities.