WIAS Preprint No. 1145, (2006)

Regression methods in pricing American and Bermudan options using consumption processes


  • Belomestny, Denis
  • Milstein, Grigori N.
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 60H30 65C05 91B28


  • American and Bermudan options, low and upper bounds, Monte Carlo method, consumption process, regression methods, optimal stopping times




Here we develop methods for efficient pricing multidimensional discrete-time American and Bermudan options by using regression based algorithms together with a new approach towards constructing upper bounds for the price of the option. Applying sample space with payoffs at the optimal stopping times, we propose sequential estimates for continuation values, values of the consumption process, and stopping times on the sample paths. The approach admits constructing both low and upper bounds for the price by Monte Carlo simulations. The methods are illustrated by pricing Bermudan swaptions and snowballs in the Libor market model.

Appeared in

  • Quant. Finance, 9 (2009) pp. 315--327.

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