The only definition offered for φάντασμα by the very comprehensive A Greek-English Lexicon of the New Testament (BDAG) is "apparition, especially ghost". As such, we should be cautious of any other interpretation. None-the-less, let's examine the evidence for (near) contemporary belief in ghosts:
A common belief: evidence
Meyer's Commentary suggests that the belief in "apparitions" was common in Jesus' time. He cite's Plato's Phaedo
And, my friend, we must believe that the corporeal is burdensome and heavy and earthly and visible. And such a soul is weighed down by this and is dragged back into the visible world, through fear of the invisible and of the other world, and so, as they say, it flits about the monuments and the tombs, where shadowy shapes of souls have been seen, figures of those souls which were not set free in purity but retain something of the visible; and this is why they are seen.
Euripides' Hecuba (a ghost delivers the entire opening monologue), and Lucian's Philopseudes
'We were only trying,' he said, 'to convince this man of adamant that there are such things as supernatural beings and ghosts, and that the spirits of the dead walk the earth and manifest themselves to whomsoever they will.'
as examples in Greek culture.
Arguably, the most relevant example from the Old Testament (Apocrypha) occurs in Wisdom, which was written 100-200 years before Jesus' time.
Were partly vexed with monstrous apparitions, and partly fainted, their heart failing them: for a sudden fear, and not looked for, came upon them. (17:15 Brenton's translation)
See also Wisdom 17:3-4. Earlier examples include Deut 18:10-11
There shall not be found among you anyone who makes his son or his daughter pass through the fire, one who uses divination, one who practices witchcraft, or one who interprets omens, or a sorcerer, or one who casts a spell, or a medium, or a spiritist, or one who calls up the dead. (NASB)
Although it forbids the practice of calling them, it still is strong evidence in belief of spirits of the dead, that is ghosts.
In I Samuel 28, there is extended passage where Saul has the ghost of Samuel conjectured up by a medium.
See also Josephus' Antiquities (60-70 years after Jesus):
As these men said thus, and called upon Alexander's ghost for commiseration of those already slain, and those in danger of it, all the bystanders brake out into tears.
...And now, O thou most impudent body of mine, how long wilt thou retain a soul that ought to die, in order to appease the ghosts of my brother and my mother?
Other commentaries agree that the belief in ghosts was likely common among first century Jews. Gill's Exposition says:
The Jews, especially the sect of the Pharisees, had a notion, from whom the disciples might have their's, of spirits, apparitions, and demons, being to be seen in the night; hence that rule, "it is forbidden a man to salute his friend in the night, for we are careful, lest, "it should be a demon".'' (citing T. Bab. Megilla, fol. 3. 1. and Sanhedrim, fol. 44. 1.)
Matthew Poole says
By this it seemeth that the doctrine of spirits was not strange to that age, though they had a sect of Sadducees which denied it.
The Benson Commentary says
that the Jews in general, particularly the Pharisees, believed in the existence of spirits, and that spirits sometimes appeared, is evident from Luke 24:37; Luke 24:39, and Acts 23:8-9.
While some certainly doubted the existence of ghosts, a significant percentage (probably the majority) of the Jewish population believed in ghosts.