WIAS Preprint No. 930, (2004)

Monte Carlo evaluation of American options using consumption processes


  • Belomestny, Denis
  • Milstein, Grigori N.

2010 Mathematics Subject Classification

  • 60H30 65C05 91B28


  • American and Bermudan options, Lower and Upper bounds, Monte Carlo simulation, Variance reduction


Here we develop a new approach for pricing both continuous-time and discrete-time American options which is based on the fact that an American option is equivalent to a European option with a consumption process involved. This approach admits construction of an upper bound (a lower bound) on the true price using a lower bound (an upper bound) by Monte Carlo simulation. A number of effective estimators of the upper and lower bounds with reduced variance are proposed. The results obtained are supported by numerical experiments which look promising.

Appeared in

  • Int. J. Theor. Appl. Finance, 9 (2006) pp. 455--481.

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