I will briefly explain the technical part of the ring, and why it points towards it belonging to either an emperor or someone from the imperial family. That ring nowadays is expensive, but in the first century would have been ludicrously, comically, unfathomably expensive. Bear with me with the technical part.

Carving that without the stone exploding is hell, and that is with modern crystalographic machinery that a top jeweller would have: diamond-point instruments, high-end optics, abrasion lathes, the lot.

In order to make that ring, you first need to have a substantially large sapphire, with a substantial purity. Even though it is counterintuitive, manually carving a big stone is much more difficult than carving a small one, because there are more chances of finding an impurity, or a deformation in the crystal structure. Stones this hard (a sapphire is a fancy topaz, and that is very high on Mohs scale) are cut by percussion: you give the stone a precise wack, and pray to your favourite deity for the stone to fracture following the crystallisation line you had noticed and not other. If there is any distortion like an impurity or a crystallisation oddity, tough luck, the stone broke to pieces. This one "Caligula ring" must have received some 8-9 wacks in order to get into that shape, and one can be positively sure that it was not the first try, sapphires are very tricky.

So, someone must have given the jeweller no fewer than three sapphires of substantial size, and the money for the improbous work. That is something that was within the economic possibilities of very few people. If not Caligula, then the ring must have belonged to someone in the imperial family