How can I decompose a plain-vanilla interest rate swap into a series of FRAs?

Question

AcadiFi · Accepted Answer

The decomposition is elegant and worth understanding because it makes swap valuation intuitive. A plain-vanilla pay-fixed, receive-floating interest rate swap exchanges cash flows at multiple reset dates. Each reset date is economically a mini-FRA settlement. Consider a 2-year, semi-annual swap on $100 million where Valencourt Capital pays fixed at 4.60% and receives 6-month SOFR. There are four reset dates. At each reset, the payment is $100M × (SOFR − 0.0460) × 182/360. That's exactly the payoff of a long FRA struck at 4.60% for that particular period. ```mermaid flowchart LR A[Swap
2-year] --> B[FRA 1
0x6] A --> C[FRA 2
6x12] A --> D[FRA 3
12x18] A --> E[FRA 4
18x24] B --> F[Sum PV
= Swap value] C --> F D --> F E --> F ``` Each FRA is struck at the same fixed rate (4.60%), which differs from individual FRA breakeven rates. The swap's fixed rate is set so that the sum of the PVs of all four FRAs equals zero at inception — this is the par swap rate. Early FRAs (when the forward curve is below 4.60%) have negative PV for the fixed payer; later FRAs (when forwards are above 4.60%) have positive PV. The weighted average, using discount factors, nets to zero. This decomposition also explains why swap DV01 is large: you're holding multiple FRAs simultaneously.

How can I decompose a plain-vanilla interest rate swap into a series of FRAs?

Master Level II with our CFA Course

Related Questions

Practice Questions