I am trying to compute shocks on the forward swap rates based on shocks to the swap rate curve (aiming at repricing consistently a set of swaps and swaptions based on a shock to the swap curve):
- It seems that I cannot deduce forward swap rates by treating the swap curve as any other discount curve and computing "forward rates". Is this true, or are there some instruments that can be used to replicate a forward swap rate based on the swap curve?
- I assume that the proper way to compute the forward swap rates is to compute them based on the forward libor rates by equating present values of a fixed and floating leg on a forward start swap. However, aren't the longer term libor curves mainly bootstraped using swaps (so inderectly using the swap curve)? I feel like stuck in a circle.
- How far am I from the true forward swap rate if I just compute forward rates based on the swap rates?
- Is there a straightforward way to derive shocks on forward swap rates based on shocks of the swap rate curve?