美式期权定价的拟蒙特卡罗模拟及其方差减小技术

在研究拟蒙特卡罗方法的基础上，选择对美式期权定价有较好稳定结果的Faure序列代替原来的伪随机序列，得到了优于LSM模拟的结果，使模拟方差得到缩减。在此基础上，综合考虑蒙特卡罗模拟的方差减少技术，把控制变量技术与对偶变量技术相结合的复合方差减少技术运用到美式期权定价的过程中。通过模拟结果发现，控制变量技术对LSM模拟和LSQM模拟都能产生较理想的方差缩减效果，结合使用控制变量技术的LSQM模拟无论是在计算效率还是结果的稳定性方面，都比使用控制变量技术的LSM模拟好。如果再将控制变量技术与对偶变量技术相结合的复合方差减少技术与LSQM模拟方法相结合，得到的模拟结果则更精确。

Quasi-Monte Carlo simulation and variance reduction technique of American option pricing

Using the quasi-Monte Carlo method to choose the results of American option pricing with good stability having Faure instead of pseudo random sequences gave better results than least squares Monte Carlo (LSM) simulation, or simulation of variance reduction. On this basis, we comprehensively consider the variance reduction techniques in Monte Carlo simulation, and the choice of control technology and dual variables technology combined with composite variance reduction techniques which can be applied to the process of American option pricing. Our simulation results show that controlling the variable technology of LSM and least squares quasi-Monte Carlo (LSQM) simulation can create an ideal variance reduction effect, and the combined technology of using the control variable LSQM simulation results in both computational efficiency and stability are better than the combination with control variable LSM simulation. Adding the control variable technology and dual compound technology combines variable variance reduction techniques with LSQM simulation, and the simulation results obtained are more accurate.