WIAS Preprint No. 1071, (2005)

Enhanced policy iteration for American options via scenario selection


  • Bender, Christian
  • Kolodko, Anastasia
  • Schoenmakers, John G. M.
    ORCID: 0000-0002-4389-8266

2010 Mathematics Subject Classification

  • 60G40 62L15 91B28


  • American options, Monte Carlo simulation, optimal stopping, policy improvement


In Kolodko & Schoenmakers (2004) and Bender & Schoenmakers (2004) a policy iteration was introduced which allows to achieve tight lower approximations of the price for early exercise options via a nested Monte-Carlo simulation in a Markovian setting. In this paper we enhance the algorithm by a scenario selection method. It is demonstrated by numerical examples that the scenario selection can significantly reduce the number of actually performed inner simulations, and thus can heavily speed up the method (up to factor 10 in some examples). Moreover, it is shown that the modified algorithm retains the desirable properties of the original one such as the monotone improvement property, termination after a finite number of iteration steps, and numerical stability.

Appeared in

  • Quantitative Finance, Vol. 8, Number 2, pp. 135-146

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