[Verse 1]
When a swap begins its journey, pricing starts at zero fair
Two parties make agreement, cash flows they will share
Fixed rate meets the floating, based on market's current state
Present value of both legs must be equal at the gate
[Chorus]
Zero value at the start, that's the pricing golden rule
Fixed leg equals floating leg, it's the swap maker's tool
When rates change through time, valuation shifts around
Present value difference shows the profit to be found
[Verse 2]
Fixed leg calculation simple, known payments down the line
Discount each with spot rates, sum them up to find
Floating leg more tricky, future payments unknown
Use forward rates to estimate what cash flows will be shown
[Chorus]
Zero value at the start, that's the pricing golden rule
Fixed leg equals floating leg, it's the swap maker's tool
When rates change through time, valuation shifts around
Present value difference shows the profit to be found
[Bridge]
If rates rise up higher, fixed payer wins the day
If rates fall down lower, floating payer gets the pay
Mark to market daily, see how values swing
Discount all future flows, that's the valuation ring
[Verse 3]
Clean price at initiation, but as time goes marching on
Interest rates keep changing, fair value's never gone
Calculate both legs again with current market rates
Subtract floating from the fixed, see which side celebrates
[Chorus]
Zero value at the start, that's the pricing golden rule
Fixed leg equals floating leg, it's the swap maker's tool
When rates change through time, valuation shifts around
Present value difference shows the profit to be found
[Outro]
Swap pricing and valuation, now you know the way
Zero start, then value shifts as rates change day by day