Looking at the fluff for the Parasite, it tells of a winged Tyranid the size of a Warrior. Since a Shrike is a winged Warrior and a Tyranid Prime is an HQ Warrior, surely it follows that the Parasite is a named variant of the Tyranid Shrike Prime. Sadly no such unit exists in the codex. So let's wishlist one up!
Tyranid Shrike Prime
WS6 - BS4 - S5 - T5 - W3 - I5 - A4 - Ld10 - Sv4+
The weapon choices will be the same as a regular Shrike, while the Biomorph choices will be identical to the regular Prime. Base cost 90. Instead of the Alpha Warrior special rule, it would get Alpha Shrike. Pretty straightforward. That took me 5 minutes. Come on, GW, keep up.
As an aside, the Parasite is pretty awesome sounding if you have a bunch of spare Ripper Swarms.