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

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  • Acciaio, Beatrice
  • Larsson, Martin
  • Schachermayer, Walter

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.

Suggested Citation

  • Acciaio, Beatrice & Larsson, Martin & Schachermayer, Walter, 2017. "The space of outcomes of semi-static trading strategies need not be closed," LSE Research Online Documents on Economics 69804, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:69804
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    File URL: http://eprints.lse.ac.uk/69804/
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    References listed on IDEAS

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    1. A. Galichon & P. Henry-Labord`ere & N. Touzi, 2014. "A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options," Papers 1401.3921, arXiv.org.
    2. B. Acciaio & M. Beiglböck & F. Penkner & W. Schachermayer, 2016. "A Model-Free Version Of The Fundamental Theorem Of Asset Pricing And The Super-Replication Theorem," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 233-251, April.
    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.
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    Citations

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    Cited by:

    1. Marcel Nutz & Johannes Wiesel & Long Zhao, 2022. "Limits of Semistatic Trading Strategies," Papers 2204.12251, arXiv.org.
    2. Francesca Biagini & Alessandro Doldi & Jean-Pierre Fouque & Marco Frittelli & Thilo Meyer-Brandis, 2023. "Collective Arbitrage and the Value of Cooperation," Papers 2306.11599, arXiv.org, revised May 2024.
    3. Marcel Nutz & Johannes Wiesel & Long Zhao, 2022. "Martingale Schr\"odinger Bridges and Optimal Semistatic Portfolios," Papers 2204.12250, arXiv.org.
    4. Marcel Nutz & Johannes Wiesel & Long Zhao, 2023. "Martingale Schrödinger bridges and optimal semistatic portfolios," Finance and Stochastics, Springer, vol. 27(1), pages 233-254, January.
    5. Julian Sester, 2023. "On intermediate Marginals in Martingale Optimal Transportation," Papers 2307.09710, arXiv.org, revised Nov 2023.
    6. Julian Sester, 2023. "On intermediate marginals in martingale optimal transportation," Mathematics and Financial Economics, Springer, volume 17, number 2, February.
    7. Marcel Nutz & Johannes Wiesel & Long Zhao, 2023. "Limits of semistatic trading strategies," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 185-205, January.

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    More about this item

    Keywords

    semi-static trading strategies; semi-static completeness; semi-static replication;
    All these keywords.

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance

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