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Pricing American options via multi-level approximation methods

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  • Denis Belomestny
  • Fabian Dickmann
  • Tigran Nagapetyan
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    Abstract

    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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    File URL: http://arxiv.org/pdf/1303.1334
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1303.1334.

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    Date of creation: Mar 2013
    Date of revision: Dec 2013
    Handle: RePEc:arx:papers:1303.1334

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    Web page: http://arxiv.org/

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    1. 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.
    2. Denis Belomestny, 2009. "Pricing Bermudan options using nonparametric regression: optimal rates of convergence for lower estimates," Papers 0907.5599, arXiv.org.
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