The exponential timestepping Euler algorithm with a boundary test is adapted to simulate an expected of a function of exit time, such as the expected payoff of barrier options under the constant elasticity of variance (CEV) model. However, this method suffers from a high Monte Carlo (MC) statistical error due to its exponentially large exit times with unbounded samples. To reduce this kind of error efficiently and to speed up the MC simulation, we combine such an algorithm with an effective variance reduction technique called the control variate method. We call the resulting algorithm the improved Exp algorithm for abbreviation. In regard to the examples we consider in this paper for the restricted CEV process, we found that the variance of the improved Exp algorithm is about six times smaller than that of the Jansons and Lythe original method for the down-and-out call barrier option. It is also about eight times smaller for the up-and-out put barrier option, indicating that the gain in efficiency is significant without significant increase in simulation time.

带有边界检验的指数时步欧拉算法适用于模拟出口时间函数的期望值，例如，在恒定弹性方差（CEV）模型下，屏障期权的期望收益。但是，由于无约束样本的退出时间呈指数增长，因此该方法遭受了很高的蒙特卡洛（MC）统计误差。为了有效地减少此类错误并加快MC仿真，我们将这种算法与有效的方差减少技术（称为控制变量方法）相结合。我们将所得算法简称为改进的Exp算法。关于我们在本文中针对受限CEV流程所考虑的示例，我们发现，改进的Exp算法的方差大约是Jansons和Lythe原始方法中用于掉落式呼叫障碍选项的方差的六倍。对于上推-下推式障碍物选择，它也要小大约八倍，这表明效率的提高是可观的，而不会显着增加仿真时间。