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Detection of arbitrage opportunities in multi-asset derivatives markets

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  • Antonis Papapantoleon
  • Paulo Yanez Sarmiento

Abstract

We are interested in the existence of equivalent martingale measures and the detection of arbitrage opportunities in markets where several multi-asset derivatives are traded simultaneously. More specifically, we consider a financial market with multiple traded assets whose marginal risk-neutral distributions are known, and assume that several derivatives written on these assets are traded simultaneously. In this setting, there is a bijection between the existence of an equivalent martingale measure and the existence of a copula that couples these marginals. Using this bijection and recent results on improved Fr\'echet-Hoeffding bounds in the presence of additional information on functionals of a copula by Lux and Papapantoleon [18], we can extend the results of Tavin [33] on the detection of arbitrage opportunities to the general multi-dimensional case. More specifically, we derive sufficient conditions for the absence of arbitrage and formulate an optimization problem for the detection of a possible arbitrage opportunity. This problem can be solved efficiently using numerical optimization routines. The most interesting practical outcome is the following: we can construct a financial market where each multi-asset derivative is traded within its own no-arbitrage interval, and yet when considered together an arbitrage opportunity may arise.

Suggested Citation

  • Antonis Papapantoleon & Paulo Yanez Sarmiento, 2020. "Detection of arbitrage opportunities in multi-asset derivatives markets," Papers 2002.06227, arXiv.org, revised Nov 2021.
    • Handle: RePEc:arx:papers:2002.06227
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    References listed on IDEAS

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    1. Hans Buehler, 2006. "Expensive martingales," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 207-218.
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    Cited by:

    1. Ariel Neufeld & Julian Sester, 2023. "Neural networks can detect model-free static arbitrage strategies," Papers 2306.16422, arXiv.org, revised Aug 2024.
    2. Jonathan Ansari & Eva Lütkebohmert & Ariel Neufeld & Julian Sester, 2024. "Improved robust price bounds for multi-asset derivatives under market-implied dependence information," Finance and Stochastics, Springer, vol. 28(4), pages 911-964, October.
    3. Jonathan Ansari & Eva Lutkebohmert & Ariel Neufeld & Julian Sester, 2022. "Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information," Papers 2204.01071, arXiv.org, revised Sep 2023.
    4. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2023. "Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation," Management Science, INFORMS, vol. 69(4), pages 2051-2068, April.

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