A differential swap, or switch LIBOR swap, involves the LIBOR rates in two different currencies but with both legs denominated in the same currency. A Japanese insurance company engages in a differential swap whereby it receives the six-month Japanese yen LIBOR and pays the six-month U.S. dollar LIBOR plus 50 bp but with both legs denominated in yen. No principal is exchanged at the end. The current LIBOR for the yen and the dollar are 6% and 4%, respectively, and the principal is 100 million yen. Hence, the first swap payment will be based on a differential of 1.5% in yen [6% = (4%-0.5%)]. The current yield pick-up is 150 bp. There is no currency risk on this swap.
Provide some intuitive explanation for the pricing of such a swap, knowing that at the time, the dollar yield curve was very steep (long-term rates are much higher than short-term rates) and the yen yield curve was almost flat.
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