Asymptotic Distribution of the EMS Option Price Estimator
针对经验鞅模拟（EMS）方法在期权定价中无法直接计算标准误差的问题，本文证明EMS价格估计量具有渐近正态分布，并通过模拟验证了500条路径下该近似的有效性。
Monte Carlo simulation is commonly used for computing prices of derivative securities when an analytical solution does not exist. Recently, a new simulation technique known as empirical martingale simulation (EMS) has been proposed by Duan and Simonato (1998) as a way of improving simulation accuracy. EMS has one drawback however. Because of the dependency among sample paths created by the EMS adjustment, the standard error of the price estimate is not readily available from using one simulation sample. In this paper, we develop a scheme to estimate the EMS accuracy. The EMS price estimator is first shown to have an asymptotically normal distribution. Through a simulation study, we then find that the asymptotic normal distribution serves as a good approximation for samples consisting of as few as 500 simulation paths.