Forward Rate Agreement

A forward rate agreement fixes, today, the interest rate for a single borrowing period that begins in the future — say, the 3-month rate starting 6 months from now (dealers call that a "6x9 FRA").

No loan actually happens. At the start of the period, the agreed rate is compared with the actual market rate, and one side pays the other the difference in cash. A borrower who feared rising rates and bought the FRA gets compensated exactly when their real borrowing costs more.

The FRA is the simplest possible rate derivative — a single period, a single cash flow — which makes it the perfect classroom for understanding its big sibling, the interest rate swap: a swap is just a chain of FRAs.

Mechanics of a 6x9 FRA

• Trade date: agree rate \(K\) (say 3.50%) on notional \(N\) for the period from month 6 to month 9.
• Fixing: at month 6, observe the reference rate \(r\) (historically LIBOR/EURIBOR; now term RFRs or the compounded rate at period end).
• Settlement: buyer (rate payer) receives \(N(r-K)\delta\), discounted if paid upfront at fixing.

Reading forward rates

FRA rates are the market's implied forwards: if 6-month money costs 3.0% and 9-month money 3.2%, the 6x9 rate must make the two routes equivalent — roughly 3.6%. A steep curve means high forwards, i.e. the market charges heavily for future rate risk.

Uses

• Corporate hedging: fix the rate on the next refinancing or deposit rollover.
• Bank gap management: patch single-period mismatches between assets and liabilities.
• Speculation on meetings: pre-reform, FRAs were precise instruments on individual central-bank moves; that role now lives in STIR futures and meeting-dated OIS.

Forward rate by no-arbitrage

Replication (borrow long, lend short) forces the FRA rate to the curve-implied forward:

Valuation after inception: \(V = N\,\delta\,\big(f_{now} - K\big) P(0, t_2)\) for the buyer — a seasoned FRA is just the discounted move in the forward.

The convexity footnote

Classic FRAs settle the discounted payoff at \(t_1\) (start of period), while the natural payoff occurs at \(t_2\); under rate-dependent discounting this timing difference creates a small convexity adjustment between FRA rates and their futures-market cousins:

— futures gain from margining when rates and P&L correlate, so futures-implied rates sit above FRA/forward rates; the adjustment grows with maturity squared and volatility.

Post-reform status

With IBORs gone, single-period exposure is now traded as short OIS, RFR futures, or "single-period swaps" (SPS) — economically FRAs on compounded overnight rates, settled in arrears (no discounting quirk). The FRA's conceptual role — atomic unit of the curve — is unchanged: any curve bootstrap still conceptually decomposes swaps into these single-period forwards.