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

Zhushun Yuan and Gemai Chen
Management Science
Vol. 55, No. 8 (Aug., 2009), pp. 1438-1450
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/40539298
Page Count: 13
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Asymptotic Normality for EMS Option Price Estimator with Continuous or Discontinuous Payoff Functions
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Abstract

Empirical martingale simulation (EMS) was proposed by Duan and Simonato (Duan, J.-C, J.-G. Simonato. 1998. Empirical martingale simulation for asset prices. Management Sei. 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 Sei. 47(8) 1122-1132) when the payoffs are piece wise 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.

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