Did Jesus have a house in Capernaum?

I've always been intrigued with this verse in Mark, as suggesting that Jesus may have had a house in Capernaum:

Mark 2.15: καὶ γίνεται κατακεῖσθαι αὐτὸν ἐν τῇ οἰκίᾳ αὐτοῦ καὶ πολλοὶ τελῶναι καὶ ἁμαρτωλοὶ συνανέκειντο τῷ Ἰησοῦ καὶ τοῖς μαθηταῖς αὐτοῦ ἦσαν γὰρ πολλοὶ καὶ ἠκολούθουν αὐτῷ

And it happened that he was reclining in his house, and many tax collectors and sinners were reclining with Jesus and his disciples, for there were many who were following him . . .

This may be an example of the criterion I was recently discussing, accidental information, or material given away in passing, where a piece of data (here: Jesus had a house in Capernaum) is assumed and not narrated. However, there is another way to take the verse. Is Mark intending the reader to take the αὐτοῦ (his) with reference to Levi, who has just been called to follow Jesus? This is the way that most commentators across the centuries have taken it, but I suspect that this is under the influence of Luke, who makes this a great party in Levi's house (Luke 5.29). Incidentally, I can't help wondering how Levi had the resources to finance this big party if he had just left everything (Luke 5.28); perhaps it was long last big bash with his old mates before setting off on the road with Jesus; or perhaps by "everything", Luke means his career and his means of earning a living (cf. the same pattern in the Zacchaeus story in Luke 19.1-10, where the tax-collector is called, and Jesus invites himself to tea).

But Mark's text encourages the reader to imagine Jesus hosting the party at his own place in Capernaum. After all, he has just asked Levi to follow him (Mark 2.14) and from that point onwards, Levi is absorbed into the anonmymous following disciples group in Mark, not even listed as one of the twelve in Mark 3.13-19. Mark 2.15-18 is a new pericope in Mark, and it is probably Mark himself who has bolted this pericope onto the Call of Levi in 2.13-14, in which case he may well have inherited this tradition about Jesus partying in his house without a link with the Levi tradition.

I am not sure why we should be surprised at the note that Jesus may have had a house in Capernaum. After all, Capernaum does seem to be the hub of his mission in Galilee. Perhaps we allow ourselves to be seduced by the saying in Matt. 8.20 // Luke 9.58, "Foxes have their holes and the birds of the air have their nests . . ." But even if Jesus said that, we don't know when he said it, and it could reflect a later, itinerant stage of his mission.

If Jesus the craftsman had a career in Capernaum, perhaps this is how he got to know those later to become his disciples.

If Mark 2.1-12 also depicts Jesus at his house (2.1, ἐν οἴκῳ, "at home"), perhaps that is why he says "Child, your sins are forgiven" -- they've just dug a big hole through the roof of Jesus' house and he's going to have to get up there later on to mend it.