# Does an Interest Rate Swap has a Vega component?

I am a bit confused on how you calculate vega for Interest Rate Swap.

One argument is that IR Swap is a combination of fixed rate bond and floating rate bond. Since a bond has no vega component, IR Swap has no vega component.

Another argument is that IR Swap can be synthetically reproduced using a cap and floor. For pay fixed and receive floating side, it is a long a cap and short a floor. Since both cap and floors are options on IR, there is a vega component.

Since these two arguments contradict themselves, which is right and why is the other wrong?

Need some guidance on this.

If the strike of the floor and cap are both equal to the swap rate, and all accrual/payment frequencies, etc. are the same, then put-call partiy implies $$C_{t}-F_{t}=S_{t},$$ where $C_{t},F_{t},S_{t}$ are the values of the cap, floor and swap instruments at time $t$.
Since the (theoretical Black-Scholes) volatility is independent of the option-type, the Vegas on the LHS cancel so that the swap Vega is $0$.