Decomposing a Five-Year Swap into Its First Coupon and Forward Swap

Summary

The document explains a way to view a vanilla five-year interest rate swap as two components: its first floating coupon, already fixed from the three-month reference rate, and the remaining coupons represented by a forward-starting swap beginning three months later and running for four years and nine months. This framing helps clarify why the floating leg’s initial coupon can be separated from later swap cash flows.

It also notes the relevant market conventions in the example: floating payments occur quarterly and are set at the start of each period, while fixed payments occur semi-annually. The first fixed coupon still accrues for six months. Although the quoted statement refers to weighting components by DV01, the answer says that the role of DV01 is unclear. Thus, the decomposition is explained, but the document does not establish a DV01-based replication or explain how to calculate such weights.

Key ideas

• The first floating coupon of a swap is already set at the start of the swap period.
• The remaining cash flows can be viewed as a forward-starting swap beginning after the first floating period.
• The example uses quarterly floating payments and semi-annual fixed payments.
• The first fixed coupon still covers a six-month accrual period.
• The answer does not explain the stated role of DV01 weighting.

Tags

# Splitting a spot swap into a forward swap and a 3 month libor


# Splitting a spot swap into a forward swap and a 3 month libor












I read the following statement:

> We can construct a 5 year swap using 3 month libor combined with a 3mo-4.75yr forward swap, weighted by the dv01s of each part.

I am not sure I understand how this is the case.

Can someone please explain?

Thanks

## Answer by Dimitri Vulis (score 2)

https://quant.stackexchange.com/a/54075

What I think they're saying here...

The USD market convention is that the floating leg pays quarterly and is set at the beginning of the coupon period from 3mo libor, and the fixed leg pays semi-annually.

You can view a vanilla 5-year swap as a portfolio of two instruments with the same notional as the original swap: the first floating coupon, which is already set to 3mo libor, and all the remaining coupons, which start in 3 months and last for 4 years and 9 months. Note that the first fixed coupon still pays 6 months of accrual.

(I don't see the relevance of the dv01.)

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.