Track zero coupon maturity risk with precision. Test compounding choices, price shocks, and yield scenarios. See results above the form with helpful visuals instantly.
The result panel appears below the header and above the form after calculation.
Use the responsive input grid below. The page stays in a single-column flow, while the form shifts to three columns on large screens.
The chart updates after each calculation and highlights the active valuation point.
1) Zero coupon price:
P = F / (1 + y / m)mT
2) Implied annual yield from price:
y = m × ((F / P)1 / (mT) - 1)
3) Macaulay duration for a zero coupon bond:
DMac = T
4) Modified duration:
DMod = T / (1 + y / m)
5) Effective duration using shocked prices:
DEff = (Pdown - Pup) / (2 × P × Δy)
6) Convexity approximation:
Convexity = (Pdown + Pup - 2P) / (P × Δy²)
7) DV01:
DV01 = DMod × P × 0.0001
For a zero coupon bond, every cash flow arrives at maturity. That is why Macaulay duration exactly matches the maturity date in years.
These rows show sample zero coupon bond cases for quick reference.
| Face Value | Market Price | YTM | Years | Compounding | Macaulay Duration | Modified Duration |
|---|---|---|---|---|---|---|
| 1,000.00 | 961.54 | 4.00% | 1.00 | Annual | 1.0000 | 0.9615 |
| 1,000.00 | 863.84 | 5.00% | 3.00 | Annual | 3.0000 | 2.8571 |
| 1,000.00 | 747.26 | 6.00% | 5.00 | Annual | 5.0000 | 4.7170 |
| 1,000.00 | 502.57 | 7.00% | 10.00 | Semiannual | 10.0000 | 9.6618 |
Zero coupon duration measures how sensitive the bond price is to yield changes. Because the bond pays only once at maturity, its timing structure is simple and clean.
A zero coupon bond has only one cash flow, paid at maturity. Since every dollar arrives at one point in time, the weighted average cash flow timing equals maturity.
Modified duration adjusts Macaulay duration for yield and compounding. It estimates the percentage price change for a small yield move, making it practical for risk analysis.
Entering both lets you compare the market price with the theoretical price implied by the chosen yield. That helps identify pricing gaps and validate assumptions quickly.
DV01 estimates how much the bond price changes for a one basis point move in yield. It is useful for comparing interest rate risk across instruments.
Yes. Compounding changes the discounting pattern and therefore affects price, implied yield, modified duration, and related sensitivity measures, even for zero coupon bonds.
Convexity helps when yield moves are larger. It improves price change estimates by capturing curve effects that modified duration alone cannot fully explain.
No. Coupon bonds have multiple cash flows, so their duration formulas differ. This tool is specifically designed for zero coupon fixed income analysis.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.