Forward Rate Agreement

Table of Contents

A forward rate agreement locks the rate of a single future interest period. The lock is benchmarked to a reference IBOR index. ORE models it with the trade type ForwardRateAgreement. This note records the domain grounding, as ORE documents it in its product catalogue.

1. Identifiers

What a trader books it as, and what to grep for. The codes are the trade type catalogue's, which is what the database enforces.

Field Value
Full name Forward Rate Agreement
Short name FRA
ORE Studio product code ForwardRateAgreement
Asset class rates
Family Forward
ORE trade data node ForwardRateAgreementData
ORE documentation forwardrateagreement.tex

2. Summary

A forward rate agreement sets a fixed forward rate against a reference IBOR index rate and tenor. The difference between the forward rate and the reference rate is paid or received at the end of the contract. Interest accrues on a predetermined notional from an agreed start date to the end of the contract. No notional changes hands. ORE settles the contract on its start date.

3. Detail

3.1. What it is

ORE defines the product as follows:

A Forward Rate Agreement is a contract between two counterparties that determines a fixed forward interest rate benchmarked to a reference IBOR index rate and tenor.

Source: ORE User Guide, Products catalogue, forwardrateagreement.tex.

ORE states three properties of the contract:

Difference between the forward rate and the reference rate is to be paid/received at the end of the contract. Interest is accrued on a predetermined notional amount from an agreed upon start date to the end of the FRA contract. There are no exchanges of notional.

Source: ORE User Guide, Products catalogue, forwardrateagreement.tex.

3.2. In plain terms

A borrower who needs a loan in the future locks its rate today. The FRA then pays the difference between the locked rate and the rate that actually fixes. The contract creates no loan. The notional only scales the payment.

3.3. How it works in ORE

The trade uses the ForwardRateAgreementData block. StartDate is the date on which the FRA expires and settles. EndDate is when the forward loan or deposit ends. The difference between the two dates is the tenor of the underlying loan. Currency names the currency of the notional. Index names the benchmark rate. It has the form CCY-INDEX-TENOR, with an integer followed by D, W, M, or Y as the tenor. Overnight indices carry no tenor. LongShort sets the direction. A long position receives the agreed rate. A short position pays it. Strike is the agreed forward rate in decimal form. The value 0.05 means a rate of 5 percent. Notional is constant. It carries no accretion or amortisation.

3.4. Mathematical notes

An FRA is a forward on one IBOR fixing. At trade time the parties agree the strike. At the fixing the reference rate realises. The payoff is the difference between the two, scaled by the notional and the accrual of the period. The payment lands at the end of the contract. No principal ever moves.

3.5. What moves its value (static sensitivities)

  • The forward rate for the contract tenor and reference index.
  • The strike and the direction of the position.
  • The discount curve to the payment date.
  • The day-count convention of the accrual period.
  • The distance to the fixing date.

Before the fixing the trade moves one for one with the forward rate. The delta is one unit of rate exposure on the notional.

3.6. How the profile ages (dynamic sensitivities)

Until its fixing the trade behaves like a forward on the reference index. On the start date the reference rate fixes. The payoff becomes a known cash amount from that moment. Only discount risk remains until the payment at the end date. At the end date the cash settles and the trade stops.

3.7. Why a customer would want it

A customer locks a future borrowing or lending rate without a loan on the balance sheet. A treasurer hedges an upcoming funding need. A trader takes a view on the short end of the curve. The FRA is also the building block of swap replication. In ORE Studio a customer books forward rate agreements to value them and run sensitivities on the ORE engine.

3.8. Example

ORE's catalogue shows a long FRA on euro six-month Euribor struck at 0.1 percent:

<ForwardRateAgreementData>
    <StartDate>20161028</StartDate>
    <EndDate>20351028</EndDate>
    <Currency>EUR</Currency>
    <Index>EUR-EURIBOR-6M</Index>
    <LongShort>Long</LongShort>
    <Strike>0.001</Strike>
    <Notional>1000000000</Notional>
</ForwardRateAgreementData>

Source: ORE User Guide, Products catalogue, forwardrateagreement.tex, listing Forward Rate Agreement Data.

4. See also

Emacs 29.3 (Org mode 9.6.15)