Bootstrapping the Spot Rate Curve

Fixed Income Analytics · 3:44

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Lyrics

[Verse 1]
Government bonds are trading on the street
With different maturities, the puzzle's incomplete
We know their prices and their coupon rates
But the spot rate curve is what we need to create

Start with the shortest bond, it's plain to see
Six months to maturity, that's our key
No coupons paid, just pure discount
The spot rate's easy to account

[Chorus]
Bootstrap up, step by step we climb
One spot rate at a time
Use the known to find unknown
Build the curve from ground up home
Bootstrap up, the method's clear
Strip away what interferes
From bond prices we derive
The spot rates that keep markets alive

[Verse 2]
Now we take the one-year government note
With coupon payments, here's what we wrote
The six-month spot rate that we found before
Helps us discount the coupon floor

Present value of each payment stream
Using known spots in our scheme
The final payment gets the rate
That makes the bond price calculate

[Chorus]
Bootstrap up, step by step we climb
One spot rate at a time
Use the known to find unknown
Build the curve from ground up home
Bootstrap up, the method's clear
Strip away what interferes
From bond prices we derive
The spot rates that keep markets alive

[Bridge]
Eighteen months, two years, and more
Each new bond opens up the door
Discount every coupon flow
With the spot rates that we know

The last payment tells the tale
Of the spot rate without fail
Sequential solving is the way
Building curves day by day

[Verse 3]
Zero-coupon equivalents we create
From coupon bonds at every date
The risk-free curve emerges clean
From this bootstrapping machine

Each maturity gets its place
In the term structure we embrace
From short to long, the rates align
A perfect risk-free rate design

[Chorus]
Bootstrap up, step by step we climb
One spot rate at a time
Use the known to find unknown
Build the curve from ground up home
Bootstrap up, the method's clear
Strip away what interferes
From bond prices we derive
The spot rates that keep markets alive

[Outro]
Government bonds show us the way
To build the curve we use each day
Bootstrap method, tried and true
The spot rate curve is waiting for you

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