Forward rate agreement

In finance, a forward rate agreement (FRA) is an interest rate derivative (IRD). In particular, it is a linear IRD with strong associations with interest rate swaps (IRSs).

A forward rate agreement's (FRA's) effective description is a cash for difference derivative contract, between two parties, benchmarked against an interest rate index. That index is commonly an interbank offered rate (-IBOR) of specific tenor in different currencies, for example LIBOR in USD, GBP, EURIBOR in EUR or STIBOR in SEK. An FRA between two counterparties requires a fixed rate, notional amount, chosen interest rate index tenor and date to be completely specified.

Forward rate agreements (FRAs) are interconnected with short term interest rate futures (STIR futures). Because STIR futures settle against the same index as a subset of FRAs, IMM FRAs, their pricing is related. The nature of each product has a distinctive gamma (convexity) profile resulting in rational, no arbitrage, pricing adjustments. This adjustment is called futures convexity adjustment (FCA) and is usually expressed in basis points.

Interest rate swaps (IRSs) are often considered a series of FRAs but this view is technically incorrect due to differences in calculation methodologies in cash payments and this results in very small pricing differences.

FRAs are not loans, and do not constitute agreements to loan any amount of money on an unsecured basis to another party at any pre-agreed rate. Their nature as an IRD product creates only the effect of leverage and the ability to speculate, or hedge, interest rate risk exposure.

The cash for difference value on an FRA, exchanged between the two parties, calculated from the perspective of having sold an FRA (which imitates receiving the fixed rate) is calculated as:

where ${\displaystyle N}$ is the notional of the contract, ${\displaystyle R}$ is the fixed rate, ${\displaystyle r}$ is the published -IBOR fixing rate and ${\displaystyle d}$ is the decimalised day count fraction over which the value start and end dates of the -IBOR rate extend. For USD and EUR this follows an ACT/360 convention and GBP follows an ACT/365 convention. The cash amount is paid on the value start date applicable to the interest rate index (depending in which currency the FRA is traded, this is either immediately after or within two business days of the published -IBOR fixing rate).

For mark-to-market (MTM) purposes the net present value (PV) of an FRA can be determined by discounting the expected cash difference, for a forecast value ${\displaystyle r}$: