[Verse 1]
Forward rate agreements lock in rates today
For borrowing or lending at a future date
No cash upfront, just promises we make
To settle when the contract comes due
The buyer wants protection from rates going high
The seller bets that rates will fall or stay
Between two parties, risk is shared this way
With settlement based on what rates actually do
[Chorus]
Price it fair with no arbitrage rule
Discount future cash flows like a jewel
Settlement amount equals notional times
Rate differential over days divided by time
FRA pricing, FRA pricing
Keep it simple, no surpricing
Fair value zero at the start
That's the no-arbitrage art
[Verse 2]
To find the FRA rate that makes value zero
We use the forward rates from yield curve hero
From spot rates today, we can derive
The future rate that keeps the deal alive
If three month LIBOR in six months' time
Should theoretically be our baseline rhyme
That's the FRA rate that balances out
Both buyer and seller without any doubt
[Chorus]
Price it fair with no arbitrage rule
Discount future cash flows like a jewel
Settlement amount equals notional times
Rate differential over days divided by time
FRA pricing, FRA pricing
Keep it simple, no surpricing
Fair value zero at the start
That's the no-arbitrage art
[Bridge]
When settlement day arrives at last
Compare the actual rate to what we forecast
If actual's higher than the FRA
Buyer receives, seller pays away
If actual's lower than agreed
Seller gets paid for the buyer's need
[Verse 3]
Value changes as time moves along
And market rates prove right or wrong
Mark to market every single day
Shows unrealized gain or loss in play
The formula stays fundamentally sound
Present value keeps us safe and sound
Discount expected settlement back
At current rates to stay on track
[Chorus]
Price it fair with no arbitrage rule
Discount future cash flows like a jewel
Settlement amount equals notional times
Rate differential over days divided by time
FRA pricing, FRA pricing
Keep it simple, no surpricing
Fair value zero at the start
That's the no-arbitrage art
[Outro]
Forward rates and present value too
No arbitrage will see you through
FRA pricing made clear and bright
Now you've got the formula right