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

• 成果类型: Article
• 署名作者: Yuan, Zhushun; Chen, Gemai
• 署名单位: University of Calgary
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.1090.1036
• 发表日期: 2009
• 页码: 1438-1450
• 关键词: empirical martingale simulation; Monte Carlo; Black-Scholes; GARCH; options; regression analysis; Asymptotic Normality; coverage rate

摘要

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.