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Hedging under an expected loss constraint with small transaction costs

Author

Listed:
  • Bruno Bouchard

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

  • Ludovic Moreau

    (D-MATH - Department of Mathematics [ETH Zurich] - ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich])

  • Mete H. Soner

    (D-MATH - Department of Mathematics [ETH Zurich] - ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich])

Abstract

We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small transactions is used to obtain a tractable model. A general expansion theory is developed using the dynamic programming approach. Explicit formulae are also obtained in the special cases of an exponential or power loss function. As a corollary, we retrieve the asymptotics for the exponential utility indifference price.

Suggested Citation

  • Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2016. "Hedging under an expected loss constraint with small transaction costs," Post-Print hal-00863562, HAL.
    • Handle: RePEc:hal:journl:hal-00863562
    Note: View the original document on HAL open archive server: https://hal.science/hal-00863562v2
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Johannes Muhle-Karbe & Max Reppen & H. Mete Soner, 2016. "A Primer on Portfolio Choice with Small Transaction Costs," Papers 1612.01302, arXiv.org, revised May 2017.
    2. Bouchard, Bruno & Muhle-Karbe, Johannes, 2022. "Simple bounds for utility maximization with small transaction costs," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 98-113.
    3. Bruno Bouchard & Johannes Muhle-Karbe, 2018. "Simple Bounds for Utility Maximization with Small Transaction Costs," Papers 1802.06120, arXiv.org, revised Mar 2021.
    4. Bruno Bouchard & Johannes Muhle-Karbe, 2022. "Simple Bounds for Transaction Costs," Post-Print hal-01711371, HAL.
    5. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2023. "Backward Hedging for American Options with Transaction Costs," Papers 2305.06805, arXiv.org, revised Jun 2023.
    6. Bruno Bouchard & Johannes Muhle-Karbe, 2018. "Simple Bounds for Transaction Costs," Working Papers hal-01711371, HAL.
    7. Lin, Zhongguo & Han, Liyan & Li, Wei, 2021. "Option replication with transaction cost under Knightian uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).

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