It depends, options can move quite a bit. Obviously in $ terms the movements are quite small, but in % terms the moves can be really big.
For example, a Jun 116 put on SPY is down $0.10 at the moment, given that it is trading at about $0.75, that's a 11.7% drop, even though SPY is virtually flat.
I'm not saying that it is an example of a "huge" move, but still it is definitely more than the stock move.