# Let $L$ denote the three-month US dollar LIBOR rate and an interest rate swap arrangement where fixed rate is $L$ and floating rate is $24\% - 2L$

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?

• 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 $24-3L = 3(8 - L)$. Apr 7 '20 at 0:32
• 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. Apr 7 '20 at 0:33