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Pricing American options via multi-level approximation methods


  • Denis Belomestny
  • Fabian Dickmann
  • Tigran Nagapetyan


In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different levels of spatial approximation and time discretization, we propose a multi-level low biased estimate for the price of an American option. It turns out that the resulting complexity gain can be rather high and can even reach the order (\varepsilon^{-1}) with (\varepsilon) denoting the desired precision. The performance of the proposed multilevel algorithm is illustrated by a numerical example of pricing Bermudan max-call options.

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  • Denis Belomestny & Fabian Dickmann & Tigran Nagapetyan, 2013. "Pricing American options via multi-level approximation methods," Papers 1303.1334,, revised Dec 2013.
  • Handle: RePEc:arx:papers:1303.1334

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    References listed on IDEAS

    1. Denis Belomestny & John Schoenmakers & Fabian Dickmann, 2013. "Multilevel dual approach for pricing American style derivatives," Finance and Stochastics, Springer, vol. 17(4), pages 717-742, October.
    2. Denis Belomestny, 2009. "Pricing Bermudan options using nonparametric regression: optimal rates of convergence for lower estimates," Papers 0907.5599,
    3. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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    Cited by:

    1. Michael Ludkovski, 2015. "Kriging Metamodels and Experimental Design for Bermudan Option Pricing," Papers 1509.02179,, revised Oct 2016.
    2. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243,
    3. repec:wsi:igtrxx:v:17:y:2015:i:01:n:s0219198915400022 is not listed on IDEAS
    4. Christian Bayer & Juho Happola & Ra'ul Tempone, 2017. "Implied Stopping Rules for American Basket Options from Markovian Projection," Papers 1705.00558,, revised Jun 2017.

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