不同基函数对LSM美式期权定价的影响

Effect of different basis functions on the LSM pricing of American option

摘要:

美式期权允许期权持有人在期权到期前的任何时间行权，因而我们无法使用B-S公式为其定价而多采用数值方法. 应用最小二乘蒙特卡洛法（LSM）对美式期权进行定价首先由Longstaff和Schwartz于2001年提出. 在该方法中，在进行最小二乘回归时，不同基函数的选取会对最终的定价结果产生重要影响.本文研究了使用不同正交多项式作为基函数对美式期权定价的影响.

Abstract:

American option allows an option holder to exercise the option at any time before the expiration of option. Thus it is impossible to price it by the B-S formula. Numerical methods are usually applied to price an American option. The least square Monte Carlo method (LSM) was firstly proposed by Longstaff and Schwartz in 2001, in which different basis functions in the least square regression can significantly affect the final pricing. In this study we discuss the effect of different basic functions on the American option pricing.