Abstract: Optimum excrcise time of an option is a very complicated metter. It is affected by manystochastic factors and so far have not been completely solved. In this paper, we discuss the optimum exercise time of an American call option by Markov transition probabilities under the supposition that stationary and uniform condition were satisfied. Sets of optimum exercise time about some common probabilitymodels have been studied. The conclusion in the theorem 3-6 can fairly suit to the actual situation of theoption exchange market. The main conclusion could be directly applied to stock and future exchange, project investment decision and some significant state strategic decision on science and technology, economy,political and military affairs and so on.

Key words: Call option, Optimum exercise time, Decision model