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Monte Carlo Evaluation Of American Options Using Consumption Processes

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Author Info

  • DENIS BELOMESTNY

    ()
    (Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr.39, D-10117 Berlin, Germany)

  • GRIGORI N. MILSTEIN

    ()
    (Department of Mathematics, Ural State University, Lenin Str. 51, 620083 Ekaterinburg, Russia)

Abstract

We develop a new approach for pricing both continuous-time and discrete-time American options which is based on the fact that any American option is equivalent to a European one with a consumption process involved. This approach admits the construction of an upper bound (a lower bound) on the true price using some lower bound (an upper bound) by Monte Carlo simulation. A number of effective estimators of upper and lower bounds with the reduced variance are proposed. The method is supported by numerical experiments which look promising.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 09 (2006)
Issue (Month): 04 ()
Pages: 455-481

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Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:04:p:455-481

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Related research

Keywords: American and Bermudan options; lower and upper bounds; Monte Carlo simulation; variance reduction;

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Cited by:
  1. Denis Belomestny & Grigori Milstein & Vladimir Spokoiny, 2009. "Regression methods in pricing American and Bermudan options using consumption processes," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 315-327.
  2. John Schoenmakers, 2012. "A pure martingale dual for multiple stopping," Finance and Stochastics, Springer, vol. 16(2), pages 319-334, April.
  3. Denis Belomestny & G. Milstein & John Schoenmakers, 2010. "Sensitivities for Bermudan options by regression methods," Decisions in Economics and Finance, Springer, vol. 33(2), pages 117-138, November.

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