Optimal Choice Models for Executing Time to American Options

Based on the structure models of options pricing on non-dividend-paying stock [16], this paper presents the choosing models and methods of optimal time of executing an American options for the first time. By using the models and methods, we can find the choosing criterion and optimal time to exercise the American options, i.e. the product of options price and its occurring probability is at maximum. So we can decide that an American option should be exercised or not in any time. The conclusions in this paper are more important in its consulting effect for single trader and organization investors to make their security market trade.