Michael Milona has an interesting discussion of the topic of whether hope can be a moral virtue. As he notes, the most common historical view in the West is that hope is a theological virtue, not a moral virtue. None of the theological virtues (faith, hope, love/charity) are moral virtues or even have close analogues among the moral virtues. This is a deliberate move, and I don't think Milona dwells on the reasons why this move is deliberately being made.
Charity is the easiest one to grasp. The closest moral analogue of charity is friendship; but friendship is not in general a virtue for the obvious reason that friendship is not in general a character trait. For friendship to be a virtue, it would have to be something a person could have, stably, in themselves, but friendship is an interaction of at least two people. However, charity, which in a sense is being friends with God, is 'infused', i.e., given by God and sustained by Him, so in having it you have friendship with God, stably, as a part of your character. Thus Scotus, for instance, calls charity 'superfriendship'; it meets the requirements of being friendship, but does so in a superabundant way normal forms of friendship do not. Thus it can be considered a virtue, although the way it fulfills the definition of virtue is somewhat different from the way that moral virtues do.
Faith and hope each have a different reasons why their closest non-theological counterparts are not virtues, although the reason why they themselves can be virtues is in a sense a different variation on the same idea. The closest non-theological counterpart to faith is belief, or reliance on human testimony; acts of reliance on human testimony could be taken up, as it were, by other virtues in specific contexts, but it is not in itself any kind of human excellence, in part because human testimony is unreliable. If faith were a nontheological virtue, it would have to perfect the intellect, but the intellect aims at truth, so what perfects or completes the intellect is guaranteed to capture some aspect of truth. This is where the intellectual virtues come in: skill, knowledge, understanding, wisdom, prudence, all of which capture some aspect of truth in a stable way. Of these, only prudence concerns matters of choice directly, so only prudence is a moral virtue. And, indeed, when we are inclined to think that this or that act of trust in human testimony is virtuous, it's usually because it is an act of prudence, although sometimes it might be an act of justice, or of fortitude, or the like. But theological faith is reliance given by God on testimony given by God, and thus it does not have the unreliability with respect to truth that human testimony does. Hope is similar, except it is concerned with good rather than true; it is concerned with good that is difficult. Nontheological hope is not a virtue because difficult good cannot be guaranteed; it is not in general a form of human excellence to act on the assumption that one already has a difficult good. (The human excellence generally concerned with difficult good is magnanimity, which is not what we would ordinarily characterize as itself being a kind of hope.) But the difficult good with which theological hope is concerned is eternal happiness, and it is a virtue given by God to trust in means given by God to achieve eternal happiness which is God Himself, and therefore it is already the beginning of what is hoped for. Theological hope has by its own means what it does not yet have in hand, and thus can have the features of a virtue.
Milona proposes a priorities account of hope: hope is having one's priorities straight. He is right, I think, that this is a virtue; it is in fact nothing other than the virtue of prudence. Milona (to his great credit) considers this possibility, but I confess I don't fully understand his argument for why they should be distinguished. I think the idea is that hope (as understood by the priorities account) is related to prudence in the way that (e.g.) justice and fortitude are, but with other virtues it's obvious why their typical acts are distinct from prudence; but it seems like deliberate setting of actual priorities is just one of the things prudence does in order to make a decision. Perhaps one could argue, though, that there is a virtue, one that could be called hope, that is a 'potential part' of prudence, as Aquinas would say, that only concerns our prioritizing. But I don't know how that would work in relation to decision-making.
