WIAS Preprint No. 1647, (2011)

Multilevel dual approach for pricing American style derivatives


  • Belomestny, Denis
  • Schoenmakers, John G. M.
    ORCID: 0000-0002-4389-8266

2010 Mathematics Subject Classification

  • 62L15 65C05 91B28


  • Optimal stopping, Dual approach, Multilevel Monte Carlo




In this article we propose a novel approach to reduce the computational complexity of the dual method for pricing American options. We consider a sequence of martingales that converges to a given target martingale and decompose the original dual representation into a sum of representations that correspond to different levels of approximation to the target martingale. By next replacing in each representation true conditional expectations with their Monte Carlo estimates, we arrive at what one may call a multilevel dual Monte Carlo algorithm. The analysis of this algorithm reveals that the computational complexity of getting the corresponding target upper bound, due to the target martingale, can be significantly reduced. In particular, it turns out that using our new approach, we may construct a multilevel version of the well-known nested Monte Carlo algorithm of Andersen and Broadie (2004) that is, regarding complexity, virtually equivalent to a non-nested algorithm. The performance of this multilevel algorithm is illustrated by a numerical example.

Appeared in

  • Finance Stoch., 17 (2013) pp. 717-742.

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