A Novel Idea to Solve Optimal Stopping Problem With Finite Time Horizon and Its Application in American Put

ABSTRACT This paper provides a novel idea to solve optimal stopping problem (OSP) with finite time horizon and hence price finite‐expiration American put. Unlike the traditional method in finding the problem to the so‐called free‐boundary problem, which causes complex calculations or numerical analysis, our proposed method is straightforward in probabilistic scheme, hence can be quickly applied to derivative pricing theory. In application, we practice the valuation of finite time horizon American put option and provide the numerical results.