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

Author

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  • Zhushun Yuan

    (Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada)

  • Gemai Chen

    (Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada)

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 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.

Suggested Citation

  • Zhushun Yuan & Gemai Chen, 2009. "Asymptotic Normality for EMS Option Price Estimator with Continuous or Discontinuous Payoff Functions," Management Science, INFORMS, vol. 55(8), pages 1438-1450, August.
    • Handle: RePEc:inm:ormnsc:v:55:y:2009:i:8:p:1438-1450
    DOI: 10.1287/mnsc.1090.1036
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    References listed on IDEAS

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    1. Wolff, Christian & Bams, Dennis & Lehnert, Thorsten, 2005. "Loss Functions in Option Valuation: A Framework for Model Selection," CEPR Discussion Papers 4960, C.E.P.R. Discussion Papers.
    2. T. Harikumar & Maria E. de Boyrie & Simon J. Pak, 2004. "Evaluation of Black-Scholes and GARCH Models Using Currency Call Options Data," Review of Quantitative Finance and Accounting, Springer, vol. 23(4), pages 299-312, December.
    3. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO.
    4. Jin-Chuan Duan & Geneviève Gauthier & Jean-Guy Simonato, 2001. "Asymptotic Distribution of the EMS Option Price Estimator," Management Science, INFORMS, vol. 47(8), pages 1122-1132, August.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    7. Wei, J.Z. & Duan, J.C., 1999. "Pricing Foreign Currency and Cross-Currency Options Under GARCH," Rotman School of Management - Finance 99-01, Rotman School of Management, University of Toronto.
    8. Jin-Chuan Duan & Jean-Guy Simonato, 1998. "Empirical Martingale Simulation for Asset Prices," Management Science, INFORMS, vol. 44(9), pages 1218-1233, September.
    9. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
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    Cited by:

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