How to calculate bond price and yield to maturity. Bond pricing formula using spot rates and YTM, with step-by-step calculation examples.
PV of future cash flows discounted at YTM. Premium: coupon > YTM. Discount: coupon < YTM. Par: coupon = YTM.
Yields on zero-coupon bonds. Used to discount each cash flow at the appropriate maturity rate.
Future short-term rates implied by spot rates. No-arbitrage condition links spot and forward rates.
Full (dirty) price = Flat (clean) price + Accrued interest. Quoted price is usually clean.
Bond Price (YTM)
Where: y = YTM per period
Bond Price (Spot Rates)
Where: S<sub>t</sub> = spot rate for maturity t
Accrued Interest
Where: Linear interpolation between coupon dates
Full Price
Where: What the buyer actually pays
Bond Price
PV of coupons + PV of par
Current Yield
Income return only
YTM
Total return if held to maturity
Macaulay Duration
Weighted average time to receive CFs
Modified Duration
Price sensitivity to yield change
Price Change (Duration)
First-order approximation
Price Change (with Convexity)
More accurate for large yield changes
Effective Duration
For bonds with embedded options
Credit Spread
Compensation for credit risk
Expected Loss
PD=prob default, LGD=loss given default
Use when:
Avoid when:
A bond trading at a premium has:
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