How is a forward rate agreement (FRA) priced and what does the fixed rate represent?

Question

AcadiFi · Accepted Answer

A forward rate agreement is essentially a bet on a future short-term interest rate. When Nordheim Capital quotes you a 3x9 FRA at 4.85%, they're offering to lock in the 6-month rate that will prevail 3 months from today.

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Suppose the 3-month spot rate is 4.20% and the 9-month spot rate is 4.58% (both on a simple-interest basis with a 360-day year). A lender could either (a) invest for 9 months directly, or (b) invest for 3 months and roll into a 6-month deposit at the FRA rate. These strategies must return the same amount or arbitrage exists. Solving (1 + 0.0420 × 90/360)(1 + FRA × 180/360) = (1 + 0.0458 × 270/360) gives the breakeven FRA rate near 4.74%.

The fixed rate represents the market's forward-looking expectation (adjusted for term premia) of where the 6-month reference rate will print on the fixing date. Neither party pays anything at initiation because both legs have equal present value. At expiry, only the difference between the FRA rate and the realized reference rate is settled, discounted back because settlement occurs at the start of the reference period rather than the end.

For deeper coverage of derivatives pricing, explore our CFA Level II derivatives module.

How is a forward rate agreement (FRA) priced and what does the fixed rate represent?

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