Is it possible to hedge an amortising interest rate swap (linearly decreasing notional) with a series of vanilla interest rate swaps? With the amortising swap originated today at par rate and the vanilla swaps also being at par.
I tried by having a series of swaps equal to the number of fixed leg payments and matching the cashflow on the fixed leg side. This is simple enough, but the end result is series of swaps each with different notional - which means that there is a notional mismatch on the floating leg and while the PVs of both the amortising swap and the series of swaps are the same they are clearly not equivalent.
Equally if we start from the floating side and determine the notionals on the swaps to be in line with the amortisation schedule, we end up with mismatches on the fixed side.
Does it mean that amortising swap cannot be hedged using vanilla swaps? Needing adding bonds to the mix?
I find that a highly surprising result, but cannot identify how to do it.