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BY 4.0 license Open Access Published by De Gruyter Open Access December 30, 2021

Detection of arbitrage opportunities in multi-asset derivatives markets

  • Antonis Papapantoleon EMAIL logo and Paulo Yanez Sarmiento
From the journal Dependence Modeling


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.

MSC 2010: 91G20; 62H05; 60E15


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Received: 2020-02-12
Accepted: 2021-11-10
Published Online: 2021-12-30

© 2021 Antonis Papapantoleon et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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