  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.
