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Detection of arbitrage opportunities in multi-asset derivatives markets

Author

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  • Papapantoleon Antonis

    (Delft Institute of Applied Mathematics, TU Delft, 2628 Delft, TheNetherlands; Institute of Applied and Computational Mathematics, FORTH, 70013 Heraklion, Greece)

  • Sarmiento Paulo Yanez

    (Institute of Mathematics, TU Berlin, Straße des 17. Juni 136, 10623Berlin, Germany)

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 Fréchet–Hoeffding bounds in the presence of additional information on functionals of a copula by [18], we can extend the results of [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

  • Papapantoleon Antonis & Sarmiento Paulo Yanez, 2021. "Detection of arbitrage opportunities in multi-asset derivatives markets," Dependence Modeling, De Gruyter, vol. 9(1), pages 439-459, January.
    • Handle: RePEc:vrs:demode:v:9:y:2021:i:1:p:439-459:n:18
    DOI: 10.1515/demo-2021-0121
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.

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