50th ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications
Management Science
Asymptotic distribution of the EPMS estimator for financial derivatives pricing
Computational Statistics & Data Analysis
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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.