重要性抽样在离散障碍期权定价中的应用

摘要

随着我国利率市场化脚步的加快,用随机过程来刻画市场利率的行为能够很好地帮助金融机构对利率衍生品进行定价,这对我们国家衍生品市场的发展是至关重要的.首先,在Vasicek利率模型下对普通债券、欧式看涨期权的定价公式进行推导.接下来,在其基础上对离散障碍期权进行定价,并运用条件期望和重要性抽样等方差缩减方法进行优化.最后,设计数值实验来进行分析.结果表明,利用条件期望、重要性抽样两种方差缩减技术的蒙特卡罗模拟方法能够对离散障碍期权进行稳定的定价.%With the development of interest rate marketization,by using of the stochastic processes to characterize market interest rates can help financial institutions to price interest derivatives,which is essential for the development of our national derivatives market.This paper first prices formula of ordinary bond and European call option under Vasicek interest rate model.Then,the discrete barrier option is priced and optimized by using the variance reduction method,such as conditional expectation and importance sampling.Finally,numerical experi-ments are designed to analyze.The results show that the Monte Carlo simulation method can predict the discrete barrier option by using the conditional expectation and importance sampling.