Question

A financial firm regularly trades in ordinary swaps and forward swaps. It is now introducing a new instrument: forward contracts on newly-initiated ordinary swaps. How could the financial firm determine the proper pricing of these forward contracts using only the pricing of their other swaps and the term structure of interest rates? Could the proper forward price ever be negative?

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The forward price should reflect the fixed rate payment of the future swap that will make the price of the swap zero, as seen from today. To get this value, the present values of the cashflows from the fixed and floating legs of the forward swap should be equal zero. Of course, the forward floating legs will be based on the forward rates as seen from today. These forward rates will be discounted back to present and thus the value of the floating leg cashflows become par on the date where the floating rate will be first reset....

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