WIAS Preprint No. 1022, (2005)

Adaptive simulation algorithms for pricing American and Bermudan options by local analysis of the financial market


  • Belomestny, Denis
  • Milstein, Grigori

2010 Mathematics Subject Classification

  • 60H30 65C05 91B28


  • American and Bermudan options, Lower and Upper bounds, Monte Carlo simulations, Local analysis, Consumption


Here we develop an approach for efficient pricing discrete-time American and Bermudan options which employs the fact that such options are equivalent to the European ones with a consumption, combined with analysis of the market model over a small number of steps ahead. This approach allows constructing both upper and low bounds for the true price by Monte Carlo simulations. An adaptive choice of local low bounds and use of the kernel interpolation technique enhance efficiency of the whole procedure, which is supported by numerical experiments.

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