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The space of outcomes of semi-static trading strategies need not be closed

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  • Beatrice Acciaio
  • Martin Larsson
  • Walter Schachermayer

Abstract

Semi-static trading strategies make frequent appearances in mathematical finance, where dynamic trading in a liquid asset is combined with static buy-and-hold positions in options on that asset. We show that the space of outcomes of such strategies can have very poor closure properties when all European options for a fixed date $T$ are available for static trading. This causes problems for optimal investment, and stands in sharp contrast to the purely dynamic case classically considered in mathematical finance.

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  • Beatrice Acciaio & Martin Larsson & Walter Schachermayer, 2016. "The space of outcomes of semi-static trading strategies need not be closed," Papers 1606.00631, arXiv.org.
    • Handle: RePEc:arx:papers:1606.00631
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    References listed on IDEAS

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    1. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2013. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
    2. Mathias Beiglbock & Pierre Henry-Labord`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
    3. Mark H. A. Davis & David G. Hobson, 2007. "The Range Of Traded Option Prices," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 1-14, January.
    4. David Hobson & Martin Klimmek, 2012. "Model-independent hedging strategies for variance swaps," Finance and Stochastics, Springer, vol. 16(4), pages 611-649, October.
    5. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    6. Mathias Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
    7. Beatrice Acciaio & Mathias Beiglbock & Friedrich Penkner & Walter Schachermayer, 2013. "A model-free version of the fundamental theorem of asset pricing and the super-replication theorem," Papers 1301.5568, arXiv.org, revised Mar 2013.
    8. Beatrice Acciaio & Martin Larsson, 2015. "Semi-static completeness and robust pricing by informed investors," Papers 1510.01890, arXiv.org, revised Sep 2016.
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    Cited by:

    1. Luciano Campi & Claude Martini, 2016. "On the support of extremal martingale measures with given marginals: the countable case," Papers 1607.07197, arXiv.org, revised Mar 2019.

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