WIAS Preprint No. 1721, (2012)

Simulation based policy iteration for American style derivatives --- A multilevel approach


  • Belomestny, Denis
  • Ladkau, Marcel
  • Schoenmakers, John G. M.

2010 Mathematics Subject Classification

  • 62L15 65C05 91B28


  • Optimal stopping, Multilevel Monte Carlo, Howard policy iteration


This paper presents a novel approach to reduce the complexity of simulation based policy iteration methods for pricing American options. Typically, Monte Carlo construction of an improved policy gives rise to a nested simulation algorithm for the price of the American product. In this respect our new approach uses the multilevel idea in the context of the inner simulations required, where each level corresponds to a specific number of inner simulations. A thorough analysis of the crucial convergence rates in the respective multilevel policy improvement algorithm is presented. A detailed complexity analysis shows that a significant reduction in computational effort can be achieved in comparison to standard Monte Carlo based policy iteration.

Appeared in

  • SIAM/ASA Journal on Uncertainty Qualification, 3 (2015) pp. 460--483.

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