Option theory is one of the greatest findings in the area of the world's economics in the 20th century. The research on option pricing theory is focused on the following two aspects: one is how to design new option to satisfy the changing investment demand; the other is how to price the more and more complicated options.Pricing in incomplete market is mainly studied in this paper, especially when the stochastic volatility of stock is not constant. A new method of American option pricing with stochastic volatility is put in this paper, based on the European option pricing. The integrating of binomial probability tree and stochastic volatility matrix is used to bring forward the new method. When the process of stochastic volatility obeyed Markov process, the pricing of American option with actual volatility Ïƒ is the sum of pricings with other volatility states. The coefficient can be calculated with the volatility matrix. The arithmetic of this idea is given in this paper. At last, the numerical experiment approved the validity of this arithmetic. Pricings with stochastic rate and trade cost are given in the last paper based on correlative literature.
