[Verse 1]
When a bond is born, it promises to pay
Interest every period, principal one day
To find what it's worth in today's money
Discount all cash flows, that's the key
Present value of payments, each one has its rate
Spot rates tell us now what future dollars weigh
Sum them all together, that's your bond's true price
Mathematics never lies
[Chorus]
P-V cash flows, that's the way
Spot rates, forward rates, show the way
Y-T-M, Y-T-C, yields we need to know
Current yield's just annual, divided by the price below
Bond valuation, future to today
Present value is the way
[Verse 2]
Current yield's so simple, coupon over price
Yield to maturity assumes you hold it tight
Yield to call considers when they might pay back
Yield to worst protects you from the risks you lack
Money market uses different ways to count
Three-sixty basis, not three-sixty-five amounts
Bond equivalent yield converts it all the same
Standard comparison game
[Chorus]
P-V cash flows, that's the way
Spot rates, forward rates, show the way
Y-T-M, Y-T-C, yields we need to know
Current yield's just annual, divided by the price below
Bond valuation, future to today
Present value is the way
[Bridge]
Spot curve shows us rates for every single year
Par curve bonds at face value, yields crystal clear
Forward rates predict tomorrow's borrowing cost
Bootstrap builds the curve from bonds we've crossed
[Verse 3]
When bonds don't trade much, matrix pricing helps
Use similar bonds to price what no one sells
Arbitrage-free framework keeps the prices true
No free lunch for me or you
Start with shorter bonds to build your rates up high
Bootstrap methodology, layer by layer try
Each new bond reveals the rate that's hidden there
Building curves with perfect care
[Chorus]
P-V cash flows, that's the way
Spot rates, forward rates, show the way
Y-T-M, Y-T-C, yields we need to know
Current yield's just annual, divided by the price below
Bond valuation, future to today
Present value is the way
[Outro]
From the cash flows to the curves
Bond valuation's what we've learned
Present value saves the day
That's the bond valuation way