随机利率下条件蒙特卡罗综合加速方法及应用

主要研究CIR(cox-ingersoll-ross)随机利率模型下欧式期权定价的蒙特卡罗加速模拟问题，提出了一种新的控制变量，基于此变量结合条件蒙特卡罗方法可对普通蒙特卡罗方法有显著加速效果.理论及数值计算表明，该方法能有效地提高计算效率.同时，提出了基于条件蒙特卡罗方法求解Greeks的算法，与经典的蒙特卡罗方法比较，能更精确、稳定地求解Greeks的值.所提出的方法同样适用于一篮子期权、离散取样亚式期权等高维期权.
This paper mainly studies acceleration methods of the Monte Carlo simulation method for the pricing of European call options under the assumption of the CIR(Cox Ingersoll Ross) stochastic interest rate model. A new control variable based on the combination of the conditional expectation formula and the control variable technique is presented. The theoretical analysis and numerical results show that this method, with a new control variable, can improve the computation efficiency. Then it is applied to the computation of Greeks. The numerical results illustrate that the new method is more accurate and stable than the classical Monte Carlo method. It can also be applied to basket options, Asian option, and other high-dimension cases