期权定价是现代金融理论的重要内容之一.期权的价格通常与标的资产价格的波动率等因素有关.B-S模型中假设波动率为常数,而实际上波动率往往是一个随机过程.本文研究带随机波动率的Lévy模型下美式看涨期权的定价问题,得到了美式看涨期权的最优执行时间以及期权价格满足的偏微分方程. Option pricing is one of the important contents of modern financial theory.The price of an option is usually related to the volatility of the underlying asset price, etc. The BS model assumes that the volatility is a constant, but in fact the volatility is often a stochastic process.In this paper, The pricing of American call options under the Lévy model with stochastic volatility leads to the optimal execution time of the American call option and the partial differential equation that the option price satisfies.