[Verse 1]
When bonds have options built inside
Callable or putable they hide
A feature that can change their ways
Before their normal ending days
The issuer can call them back
Or holders put when rates attack
Regular duration fails the test
When options mess with interest
[Chorus]
Effective duration shows the way
When options come into play
It measures price sensitivity
When rates change the game we see
Not modified but effective true
For complex bonds it's what we do
The real response to rate changes
When embedded options rearrange us
[Verse 2]
Take a bond that's callable now
Interest rates drop down somehow
The issuer might call it in
Refinance at rates more thin
Regular duration overstates
How much the price appreciates
'Cause upside gains get cut away
When call options come to stay
[Chorus]
Effective duration shows the way
When options come into play
It measures price sensitivity
When rates change the game we see
Not modified but effective true
For complex bonds it's what we do
The real response to rate changes
When embedded options rearrange us
[Bridge]
Calculate with yield curve shifts
Up and down the model lifts
Price with rates up then down
See how much the bond moves around
Divide the difference by the change
Times the base price in the range
That's effective duration's call
For bonds with options after all
[Verse 3]
Putable bonds work the reverse
When rates go up they could disburse
Holders put them back for par
Protection when yields climb too far
So downside risk gets limited
Regular duration's not fitted
Effective shows the real impact
When option features make their pact
[Chorus]
Effective duration shows the way
When options come into play
It measures price sensitivity
When rates change the game we see
Not modified but effective true
For complex bonds it's what we do
The real response to rate changes
When embedded options rearrange us
[Outro]
For complex bonds remember well
Effective duration's tale to tell
When options embedded deep inside
Let effective be your guide