Asymptotic Normality for EMS Option Price Estimator with Continuous or Discontinuous Payoff Functions

Empirical martingale simulation (EMS) was proposed by Duan and Simonato (Duan, J.-C., J.-G. Simonato. 1998. Empirical martingale simulation for asset prices. Management Sci.44(9) 1218--1233) as an adjustment to the standard Monte Carlo simulation to reduce simulation errors. The EMS price estimator of derivative contracts was shown to be asymptotically normally distributed in Duan et al. (Duan, J.-C., G. Gauthier, J.-G. Simonato. 2001. Asymptotic distribution of the EMS option price estimator. Management Sci.47(8) 1122--1132) when the payoffs are piecewise linear and continuous. In this paper, we extend the asymptotic normality result to more general continuous payoffs, and for discontinuous payoffs we make a conjecture.