Detection of arbitrage opportunities in multi-asset derivatives markets

Papapantoleon Antonis () and Yanez Sarmiento Paulo ()
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Papapantoleon Antonis: Delft Institute of Applied Mathematics, TU Delft, 2628 Delft, The Netherlands; Institute of Applied and Computational Mathematics, FORTH, 70013 Heraklion, Greece
Yanez Sarmiento Paulo: Institute of Mathematics, TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany

Dependence Modeling, 2021, vol. 9, issue 1, 439-459

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.

Keywords: Arbitrage; equivalent martingale measures; detection of arbitrage opportunities; multiple assets; multi-asset derivatives; copulas; improved Fréchet–Hoeffding bounds (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:9:y:2021:i:1:p:439-459:n:18

DOI: 10.1515/demo-2021-0121

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