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Empirical Martingale Simulation for Asset Prices

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  • Jin-Chuan Duan

    (Department of Finance, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Jean-Guy Simonato

    (École des Hautes Etudes Commerciales, 3000, Chemin de la Côte-Sainte-Catherine, Montréal, Quebec, Canada H3T 2A7)

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    Abstract

    This paper proposes a simple modification to the standard Monte Carlo simulation procedure for computing the prices of derivative securities. The modification imposes the martingale property on the simulated sample paths of the underlying asset price. This procedure is referred to as the empirical martingale simulation (EMS). The EMS ensures that the price estimated by simulation satisfies the rational option pricing bounds. The EMS yields a substantial error reduction for the price estimate and can be easily coupled with the standard variance reduction methods. Simulation studies are conducted for European and Asian call options using both the Black and Scholes and GARCH option pricing frameworks. The results indicate that the EMS yields substantial variance reduction particularly for in- and at-the-money or longer-maturity options. The option price estimate based on the EMS is found to exhibit a minor small-sample bias only in few occasions. An analysis of the trade-off between computing time and price accuracy reveals that the EMS dominates the conventional simulation methods.

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    File URL: http://dx.doi.org/10.1287/mnsc.44.9.1218
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 44 (1998)
    Issue (Month): 9 (September)
    Pages: 1218-1233

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    Handle: RePEc:inm:ormnsc:v:44:y:1998:i:9:p:1218-1233

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    Related research

    Keywords: Martingale; Option Pricing; Monte Carlo Simulation; GARCH; Asian Options;

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