Pathwise derivative methods on single-asset American option sensitivity estimation

Abstract

In this paper, we investigate efficient Monte Carlo estimators to American option sensitivities on single asset. Using two features of the exercising boundary of the optimal stopping problem, the “continuous-fit” and “smooth-pasting” conditions, we derive unbiased pathwise estimators for first and second-order derivatives. Our method can be easily embedded into some popular algorithms for pricing one-dimensional American options. Numerical examples on vanilla puts illustrate accuracy and efficiency of the method.