Can someone please elaborate on how duration of swaps is affected by changes in interest rates? I am sure its not completely linear. Can someone please explain?
Think about in terms of: Pay Fixed Swap= Floating Rate Bond - Fixed Rate Bond So DBond/DR= DFloater/DR - DFixed/DR as DFixed/DR and DFloater/DR doesn’t equal DFixed/DR plus a constant, the duration isn’t constant…
I believe the duration depends on which side of the SWAP. Fixed or Floating. For floating receiver, the duration is usually half of the settlement period. (if the 6 month settlement, the duration will be about 0.5/2=0.25). For fix receiver, the duration is the same as the bond-like fix cashflow-producing fix SWAP. A 6-month settle fix payment for 4 years SWAP is like a 4yr semiannual bond.
ook so would the duration of the swap increase with increase in interest rates and vice versa ?
For the floating coutnerparty in a swap duration shouldn’t really change. For fixed, I believe your duration would become longer. Think of how you calculate duration. Duration = the weighted average of the present value of the cash flows. Because you Pv the cashflows, if you drop the discount rate (interest) duration should become longer. All else equal.
Now wait a minute - the duration is the sensitivity to interest rate movements. The fixed and floating have to have the same duration (with different sign) because if interest rates move one side is making the money the other loses.
yes but swaps are a series of payments. The floating duration of a swap is essentially the amount of time until the next payment, the fixed portion’s duration will change with interest rate movements, the passage of time etc.