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[CFA Level 1] 为什么说swap是一系列的FRA组成

看了英文版的note解释,还是一知半解。

“The difference between a fixed-for-floating swap and a series of forward contracts is that all the fixed-rate payments in a swap are equal. A swap can be replicated by a series of forward contracts that expire on each of the swap’s payment dates, but the fixed rates on these forward contracts are not necessarily equal.”

“ However, there is one important difference. Because the forward contract rates are all equal in the FRAs that are equivalent to the swap, these would not be zero value forward contracts at the initiation of the swap.”  出自note

疑问:fixed rate on forward contract不就是 forward contract rate嘛,那为何两句红色部分矛盾?还是我理解错了

Consider a one-year swap with quarterly payments, one party paying a fixed rate and the other a floating rate of 90-day Libor. At each payment date the difference between the swap fixed rate and Libor (for the prior 90 days) is paid to the party that owes the least, that is, a net payment is made from one party to the other.
We can separate these payments into a known payment and three unknown payments which are equivalent to the payments on three forward rate agreements.

疑问:分成90days from now based on 90-day libor的FRA, 180days 90-day LIBOR FRA-2,270 days 90-day LIBOR FRA 3, 360days 90-day LIbor FRA.

那为何第一次payment是known呢?

1. FRAs in a swap are different from FRAs on the run, which are called off-market forwards. An off-market forward is one in which the forward price is different from that which gives the forward a zero value at initiation. That means an interest rate swap is a series of off -market forward rate agreements. Some of them have a positive value to the long, while others have a negative value. When the values of all the off-market FRAs are summed together as a swap, the swap has a value of zero (at initiation).

2.  With a swap, the next payment is always known one period ahead, when the floating rate for the next period becomes known. This is not true for an FRA, because its payment is made at expiration, based on the 1-period rate for the next period.

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