Detection of arbitrage opportunities in multi-asset derivatives markets

Antonis Papapantoleon and Paulo Yanez Sarmiento

Papers from arXiv.org

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.

Date: 2020-02, Revised 2021-11
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Citations: View citations in EconPapers (4)

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