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Les bandes de Bollinger comme technique de réduction de la variance des prix d’options sur obligations obtenus par la simulation de Monte-Carlo

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  • Théoret, Raymond

    (École des sciences de la gestion)

  • Rostan, Pierre

    (Audencia, École de management)

Abstract

In this paper, we propose a new variance reduction technique to speed up the convergence during a Monte-Carlo simulation : Bollinger Bands. Beside being used in technical analysis, we show how Bollinger Bands can filter the extreme variations appearing during a simulation. We apply this technique in conjunction with the Fong and Vasicek model to price bond options (OBK) traded at the Montreal Exchange. The MSE is drastically reduced when adding Bollinger Bands to the simulation. In addition, the Fong and Vasicek model in conjunction with the Bollinger Band-based technique performs very well compared to the Black, Derman and Toy model, a widespread model among professionals. Dans cet article, nous proposons une nouvelle technique de réduction de la variance d’une simulation : les bandes de Bollinger. Nous montrons comment le recours aux bandes de Bollinger, une procédure utilisée en analyse technique, peut accroître considérablement la performance d’une simulation de Monte-Carlo en termes de réduction de la variance des simulations. La technique des bandes de Bollinger sert à filtrer les variations extrêmes qui s’observent dans une simulation. Nous appliquons cette technique à la simulation des prix de 38 options sur obligations (OBK) transigées à la Bourse de Montréal, ce en tirant profit du modèle de Fong et Vasicek pour simuler les prix des options. L’erreur quadratique moyenne des simulations se voit réduite considérablement à la suite de l’utilisation des bandes de Bollinger. Le modèle de Fong et Vasicek renforcé par les bandes de Bollinger se compare également très favorablement à celui de Black, Derman et Toy, soit le modèle encore le plus utilisé dans la pratique financière pour évaluer les options sur taux d’intérêt et sur obligations.

Suggested Citation

  • Théoret, Raymond & Rostan, Pierre, 2005. "Les bandes de Bollinger comme technique de réduction de la variance des prix d’options sur obligations obtenus par la simulation de Monte-Carlo," L'Actualité Economique, Société Canadienne de Science Economique, vol. 81(4), pages 693-724, décembre.
  • Handle: RePEc:ris:actuec:v:81:y:2005:i:4:p:693-724
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