WIAS Preprint No. 1105, (2006)

An iteration procedure for solving integral equations related to the American put options


  • Belomestny, Denis
  • Gapeev, Pavel

2010 Mathematics Subject Classification

  • 65D15 91B28 60G40 65D30 60J60 60J65


  • American put option, Black-Scholes model, optimal stopping, Picard iterations, upper and lower bounds


A new algorithm for pricing American put option in the Black-Scholes model is presented. It is based on a time discretization of the corresponding integral equation. The proposed iterative procedure for solving the discretized integral equation converges in a finite number of steps and delivers in each step a lower or an upper bound for the price of discretized option on the whole time interval. The method developed can be easily implemented and carried over to the case of more general optimal stopping problems.

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