控制变量技术在美式期权定价中的应用

全球期权交易大多是美式期权，但美式期权的路径依赖特征导致其比欧式期权定价更具复杂性。Black-Scholes定价模型对美式看跌期权不存在解析公式，无法求其精确解。一些比较成熟的数值计算方法对美式期权定价有局限性：如Monte Carlo模拟法是前导程序，而美式期权的边界是自由的，故Monte Carlo模拟法不能正确对其定价；二叉树定价模型虽然适合各种期权估价，但存在缺陷，如精度问题。控制变量技术是一种方差缩减方法，利用控制变量技术修正二叉树定价模型定价的美式期权价值，可以提高美式期权估值的精度。

An Application of the Control- variant Approaches in the American Options Pricing

Most of options transactions are American-type options in the world. Due to path-dependent character, it results in more complex American options pricing than European one. Black-Scholes pricing model has no analytical formula of American put options, thus it cannot get accurate solution. Some of relatively mature numerical methods cannot reasonably estimate American options. Because Monte-Carlo simulation is a forward induction procedure and boundary of American options is free, Monte-Carlo simulation is unable to correctly value American options. Binomial tree can be applied to pricing of all kinds of options, but it has a lot of flaws, such as accuracy. So when the number of step is very small, it affects the accuracy of the American options pricing. The control-variant approaches are variance reduction techniques and improve the value of American options valued by binomial tree and increase estimation accuracy.