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Forward Rate Agreement (FRA)

An OTC contract fixing a future interest rate on a notional principal — the buyer pays fixed, receives floating at settlement.

A FRA is a cash-settled forward on a short-term interest rate (typically LIBOR or SOFR). The buyer locks in a fixed rate (r_FRA) and receives the difference if the reference rate (r_ref) settles above it. Settlement is discounted back to the start of the reference period: Settlement = (r_ref − r_FRA) × N × d/basis / (1 + r_ref × d/basis). A positive settlement means the buyer receives; negative means the buyer pays. FRAs are quoted as '3×6' (starting in 3 months, covering the 3–6 month period). CFA uses FRAs to illustrate rate locking and yield curve arbitrage.

Formula
Settlement=(rref−rFRA)×N×d/basis1+rref×d/basis\text{Settlement} = \frac{(r_{\text{ref}} - r_{\text{FRA}}) \times N \times d/\text{basis}}{1 + r_{\text{ref}} \times d/\text{basis}}
Where
rrefr_{\text{ref}}=Reference rate at settlement (e.g. SOFR)
rFRAr_{\text{FRA}}=Agreed fixed FRA rate
NN=Notional principal
dd=Days in contract period
Related Terms

Forward Rate

The implied future interest rate derived from today's zero curve — what the market 'expects' rates to be.

Interest Rate Swap (IRS)

An agreement to exchange fixed-rate cash flows for floating-rate cash flows on a notional principal.

Discount Factor (DF)

The present value of $1 receivable at a future time T, derived from the zero curve: DF = e^(−rT).

Black-Scholes-Merton Model (BSM)

The foundational option pricing formula that gives the fair value of a European call or put as a function of spot, strike, rate, volatility, and time.

Delta (Δ)

The sensitivity of an option's price to a $1 change in the underlying spot price.

Gamma (Γ)

The rate of change of delta with respect to the spot price — the curvature of the option's value.