Exercise 21.4.1 Party A wants to take out a floating-rate loan, and B wants to take out a fixed-rate loan. They face the borrowing rates below:

Fixed Floating A F A% LIBOR +SA%

B F B% LIBOR +SB%

Party A agrees to pay the bank a floating rate of (LIBOR −S

A)% in exchange for a fixed rate of (FA + F

A)%, and B agrees to pay the bank a fixed rate of (FB + F

B)%

in exchange for a floating rate of (LIBOR−S

B)%. Prove that 0 < SA + F

A

+ S

A < SA + FB − FA + F

B

+ S

B < SA + FB − SB − FA must hold for bothAand B to enter into a swap with the bank in whichAeffectively takes out a floating-rate loan and B a fixed-rate loan.