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Global Hedging through Post-Decision State Variables

Author

Listed:
  • Michèle Breton

    (Department of Decision Sciences, HEC Montréal, 3000 Chemin de la Côte-Sainte-Catherine, Montréal, QC H3T 2A7, Canada)

  • Frédéric Godin

    (Department of Mathematics and Statistics, Concordia University, 1455 Boulevard de Maisonneuve O, QC H3G 1M8, Canada)

Abstract

Unlike delta-hedging or similar methods based on Greeks, global hedging is an approach that optimizes some terminal criterion that depends on the difference between the value of a derivative security and that of its hedging portfolio at maturity or exercise. Global hedging methods in discrete time can be implemented using dynamic programming. They provide optimal strategies at all rebalancing dates for all possible states of the world, and can easily accommodate transaction fees and other frictions. However, considering transaction fees in the dynamic programming model requires the inclusion of an additional state variable, which translates into a significant increase of the computational burden. In this short note, we show how a decomposition technique based on the concept of post-decision state variables can be used to reduce the complexity of the computations to the level of a problem without transaction fees. The latter complexity reduction allows for substantial gains in terms of computing time and should therefore contribute to increasing the applicability of global hedging schemes in practice where the timely execution of portfolio rebalancing trades is crucial.

Suggested Citation

  • Michèle Breton & Frédéric Godin, 2017. "Global Hedging through Post-Decision State Variables," JRFM, MDPI, vol. 10(3), pages 1-6, August.
    • Handle: RePEc:gam:jjrfmx:v:10:y:2017:i:3:p:16-:d:107638
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    References listed on IDEAS

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    Cited by:

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