This paper mainly analyzes the influence of different factors on the price of American call option and put option and European call option and put option. This paper mainly considers the option premium from four aspects: strike price, up factor, down factor, and interest rate. First, this paper discusses the possible situation of stock prices in different periods, and then gives the corresponding market decisions and the consequences of the corresponding market decisions according to different

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... ituations. In each case, this paper shows the process of option premium change through binomial tree diagram and a lot of formula analysis, and then compares the American option with the European option. Through this paper, people can have a basic understanding of American option and European option, and people can have a deeper understanding of the operating logic behind them.