基于方差缩减的高维美式期权Monte Carlo模拟定价

摘要

American options allow holders to execute an order at any moment before due date.However, the pricing of American options is comparatively complicated because it involves the optimal stopping rule.Monte Carlo method is flexible and easy to implement.Besides, its error estimation and convergence rate are independent of the dimension of the problem, providing Monte Carlo method a great advantage over classical numerical approaches in option pricing.This paper combines the Least Square Monte Carlo method with some variance reduction techniques and a memory reduction approach to price multi-asset American-style options, then compares the efficiency of different variance reduction techniques, and analyzes their application.%美式期权给予持有者在到期日之前任何时刻的权利,因涉及最佳执行时刻问题定价较为复杂.Monte Carlo方法其估计误差及收敛速度与问题的维数独立,可较好地处理高维衍生证券问题,且方法灵活易于实现.利用最小二乘蒙特卡洛方法(LSM),结合存储量减小技术与方差缩减技术,将 Monte Carlo 模拟方法应用于多标的资产的美式期权定价,并比较、分析了不同方差缩减技术的效果及适用范围.