随着金融市场的不断发展，期权逐渐成为一种流行广泛 的金融衍生品。为满足市场需求，在传统期权的基础上产生了各类的 路径依赖型奇异期权，收益取决于标的资产有效期内平均价格的亚式 期权就是其中很好的一例。为使期权交易在金融市场有序进行，期权 定价成为一项关键性课题。本文基于建立在Black-Scholes 模型上的 期权定价方法，首先对模型解析法和蒙特卡洛模拟方法这两种解法进 行分析，发现了它们假定标的资产价格连续和对于解析法有时过于复 杂无法求解的缺陷以及它们只适用于欧式期权定价的局限。接着，在 此基础上，引用并完善了跳跃扩散模型使得标的资产价格走势具有跳 跃性从而更符合实际市场，并通过总体最小二乘蒙特卡洛方法进行逆 向模拟完成对期权交易最优停时和最大收益的确定，由此对美式-亚 式期权进行定价。最后，通过实例模拟，验证了总体最小二乘蒙特卡 洛方法的准确和高效性。

With the development of the financial market, options have become a kind of popular derivatives. To meet the market demand, people produced path-dependent options which derived from the standard options. Asian option whose income depends on the average price during the valid time takes a good example. To make options trade in an orderly manner, option pricing has become a key issue. Previous studies dealing with option pricing usually assumed that the process of underlying asset is continuous and they used the analytical method and Monte Carlo method to get the result. However, sometimes it is hard to get a analytical solutions and also these two methods only apply to European option. This paper does the research to improve the defect. First, the paper applies jump diffusion process to model the underlying assets. Then, the paper creats total least squares Monte Carlo method which presents a method to price the option under the model. Last, by the example simulation, the paper verifies the accuracy and efficiency of the total least squares Monte Carlo method.