分数布朗运动环境下的美式看涨期权的定价方法

American Call Option Pricing Method in Fractional Brownian Motion Environment

在分数布朗运动模拟算法基础上,提出了分数布朗运动环境下标的资产价格过程的一种数值模拟方法。然后应用于欧式和美式看涨期权定价。结果表明,该方法具有很快的收敛速度,而且基于最小二乘方法和偏最小二乘方法的美式看涨期权价格,都与对应的欧式看涨期权价格几乎完全一样。这恰恰验证了不支付红利的条件下,美式看涨期权不应该提前执行的理论论断。

In this paper,on the basis of simulation algorithms for fractional Brownian motion ,we discuss a numerical simulation method for underlying asset price process in fractional Brownian motion environment,and then apply to European call option and American call option.The result indicates that this method has high converge speed, moreover the prices of American call option based on least-squares regression approach and partial least-squares regression approach are almost the same as European call option which corresponding,and they validate nicely theory judgment that American call option should not administer ahead of schedule under the condition of having no dividend payment.