Asymptotic distribution of the EMS option price estimator

Monte Carlo simulation is commonly used for computing prices of derivative securities when an analytical solution does not exist. Recently, a new simu lation technique known as empirical martingale simulation (EMS) has been pr oposed by Duan and Simonato (1998) as a way of improving simulation accurac y. EMS has one drawback however. Because of the dependency among sample pat hs created by the EMS adjustment, the standard error of the price estimate is not readily available from using one simulation sample. In this paper, w e develop a scheme to estimate the EMS accuracy. The EMS price estimator is first shown to have an asymptotically normal distribution. Through a simul ation study, we then find that the asymptotic normal distribution serves as a good approximation for samples consisting of as few as 500 simulation pa ths.