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The following is a question taken from Heard on the Street.

Let $L$ denote the three-month US dollar LIBOR rate. Consider an interest rate swap arrangement where Party A pays $L$ to Party B, and Party B pays $24\% - 2L$ to Party A. Can you reverse engineer this deal and express it in simpler terms?

The answer given is as follows:

If you subtract LIBOR, denoted $L$, from both payments, it seems that Party B is paying $24\% − 3L$. This is three times $8\% − L$. The quoted swap is, therefore, equivalent to three swaps, each of which is a swap of LIBOR for $8\%$ fixed (where Party A pays LIBOR, and Party B pays $8\%$).

I do not understand the solution given. Why do we subtract $L$ for both parties? After subtraction, why can we deduce that the quoted swap is equivalent to three swaps and the fixed rate of each swap?

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  • $\begingroup$ Implicit is the assumption that the swap payments are contemporaneous. At each swap payment, $A$ loses $L$ but gains $24-2L$, i.e. a pnl of $24-3L = 3(8 - L)$. $\endgroup$
    – user217285
    Apr 7 '20 at 0:32
  • $\begingroup$ To more directly answer your question, you get to "subtract $L$" for both parties because if each party's payment increases/decreases by the same amount, they net out. The $L$ "subtracted" from me is given to the counterparty, which is netted out when you subtract $L$ from the counterparty's payment. If I owe you 5 dollars and you owe me 10, it's the equivalent of me owing you 3 dollars and you owing me 8. $\endgroup$
    – user217285
    Apr 7 '20 at 0:33

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