Backward simulation methods for pricing American options under the CIR process
研究了CIR过程的向后模拟方法，解决了最小二乘蒙特卡洛方法在美式期权定价中的内存需求问题，提出了多种向前向后模拟方案并进行了数值测试。
In this paper, we focus on backward simulation of the CIR process. The purpose is to solve the memory requirement issue of the Least Squares Monte Carlo method when pricing American options by simulation. The concept of backward simulation is presented and it is classified into two types. Under the framework of the second type backward simulation, we seek the solutions for the existing CIR schemes. Specifically, we propose forward–backward simulation approaches for Alfonsi’s two implicit schemes, the fixed Euler schemes and the exact scheme. The proposed schemes are numerically tested and compared in pricing American options under the Heston model and the stochastic interest rate model. Some numerical properties such as the convergence order of the explicit–implicit Euler schemes, the storage requirement estimation of the forward–backward exact scheme and its computing time comparison with the squared Bessel bridge are also tested. Finally, the pros and cons of the related backward simulation schemes are summarized.