分层MC在期权定价中的应用
Application of Layered MC in Option Pricing
摘要:
本文从理论上分析了利用分层MC抽样技术可以提高模拟的计算精度，以及推导了分层抽样方差缩减的效果(通过VRERS值或粗糙估计量方差的比较)，给出了分层MC模拟的具体算法；且根据推导发现分层概率加权方法、分层匹配样本方法与最优分层方法这三种方法中，最优分层方法方差缩减效果比分层匹配样本方法方差缩减效果好。并把所研究的成果应用于欧式看涨期权的定价之中，对于期权理论的研究和完善具有重要的基础作用。
Abstract:
This paper enhances the calculation precision and operation efficiency of stratified sampling via analyzing stratified MC sample technique in theory, deduces the effect of stratified sampling in variance reduction techniques and provides idiographic arithmetic of stratified MC simulation. Finding in the three method of stratified probability weighted, stratified matched sampling and optimal stratified sampling after deducing, the optimal stratified sampling performs well in vari-ance reduction techniques. The results also are applied in the European call option. It plays to the basic key role to the theoretical researches and perfection of the option.
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