Heh, picked up on that one did you? No, nowhere in the book does it expicitly state that you need a shield or anything else in order to parry.
BUT.... :roll:
It is insinuated in several places. The strongest is under the description for the large shield
a large shield may instead be strapped to the shoulder to allow for two weapons or a two handed weapon to be used, in which case the parry bonus is reduced to +0 due to the awkwardness involved, though it can still be used to parry in this case. Alternatively, it may be strapped to the back, in which case it may not be used to parry with but gives +2 DR against one opponent per round when the wearer is flanked.
Now the question is, why would they need that language if they didn't have a rule that said "you can only parry when holding a shield or one of the following weapons....."
My guess it that this was another playtest rule that was dropped, probably for the sake of simplicity, and never fully cleared up (like the refrences to rolling for your DV). So the way I see it you as DM have a few options.
Option the first: for simplicticy's sake let a character dodge or parry, whatever they want, regardless of what they are holding in their hands.
Option the second: for the sake of giving a nod towards realism, you may only parry if you are holding
something (even an improvised weapon, like a stick) or have Improved Unarmed Strike. It's not good to bring your empty hands to a sword-fight.
Option the third: for lots of complexity that might possibly add another tatictal element to the game. You may only parry if you are holding a shiled or one of a list of weapons. So perhaps you can parry with an arming sword but not a warhammer, or you can parry with a bill but not a pike.
As for myself I am leaning towards option 2 but may just give up and go for option 1. It probably won't make that much difference in the long run (though it could be fun and dramatic to watch a player despreatly rip the leg off a chair just because he needs something to defend himself with).
Good luck.