to clarify — this is not a round trip arbitrage. This is simply buying and selling in the same market (both transactions are official and within regulation). The anomaly here is that Bank’ cards have rates similar to parallel market rate.
The reason, to put it simply, is: card transactions are not funded by the CBN; banks source for the dollars independently (i.e. using their own resources).
So, as dollars got more scarce to purchase, they – banks – had no choice but to find other means of managing its cards’ outflow (the spending limits are obviously not having the desired effects).
As a result, increasing their cards’ rates, high enough, is meant to technically discourage usage and also allow them to charge a premium on these transactions to justify allocating a scarce resource to its funding.
Moreover, some banks, while maintaining a high rate, have restricted purchases in locations with a history of high volumes, like China and Dubai. On the other hand, a few audacious ones have gone the extreme route by banning their cards from international usage – eliminating e-demand totally.