Commodity and Interest Rate Swaps

I have come across a number of practice questions that ask if the value of a commodity swap or interest rate swap will change over time, even if market prices and/or interest rates do not change. The answer is always that yes, they will both change, because the value of a swap is the PV of a stream of cash flows. I guess what I don’t understand is, if the value of the swap is initially set to zero, and nothing changes over the life of the swap, why does its value change? If time-left-to-settlement is the only thing changing, it would seem like it would effect both parties equally. Any thoughts? Thanks

PV= 0 initially but it will fluctuate till expiration because of the following factors. - changing forward curve - changing futures price - periodic swap (e.g., immediately after you have done your first of a series of say 8 interest rate swap, the PV of the contract MAY change if PV what you have just given < PV what you have just received). Remember that PV(swap)=0 since the PV(what to be given from one side) = PV(what to be given from the other side) PV(what to be given from each side) will change if the discount rates change (forward curve), value of what to be given (futures price).