Bootstrapped results
Enter bond data and submit the form to build discount factors, spot rates, forward rates, and a yield curve chart.
Calculator inputs
Example data table
| Instrument | Maturity | Coupon % | Price | Frequency |
|---|---|---|---|---|
| ZC 0.5Y | 0.5 | 0.0 | 97.9639 | 2 |
| Bond 1Y | 1.0 | 4.4 | 100.0479 | 2 |
| Bond 1.5Y | 1.5 | 4.6 | 100.0827 | 2 |
| Bond 2Y | 2.0 | 4.8 | 100.1281 | 2 |
| Bond 2.5Y | 2.5 | 5.0 | 100.1868 | 2 |
| Bond 3Y | 3.0 | 5.2 | 100.5136 | 2 |
This sample starts with a zero-coupon node and extends into semiannual coupon bonds, which makes the recursive discount-factor extraction straightforward to verify.
Formula used
Price = Σ(CFt × DFt)
DFT = (Price − Σ(earlier coupon cash flows × known discount factors)) ÷ final cash flow
SpotT = DFT−1/T − 1
zT = −ln(DFT) ÷ T
Forward = (DFt1 ÷ DFt2)1/(t2−t1) − 1
How to use this calculator
- Enter the face value used by your bond prices, usually 100.
- Add one row per market instrument, from shortest maturity to longest maturity.
- Provide maturity, annual coupon rate, market price, and coupon frequency.
- Choose strict solving or an interpolation method for missing earlier coupon dates.
- Submit the form to derive discount factors, spot rates, and forward rates.
- Review the repriced column to confirm the recovered curve matches input prices.
- Use the chart for curve shape checks and export the solved table when needed.
FAQs
1) What does bootstrapping solve?
It extracts discount factors and spot rates one maturity at a time. Earlier bond cash flows are valued with already solved nodes, then the final unknown discount factor is isolated algebraically.
2) Why should maturities be ordered?
Bootstrapping is recursive. A later bond often pays coupons before maturity, so those earlier dates need known discount factors first. Ordering the list shortest to longest avoids unsolved intermediate cash-flow dates.
3) Can I use zero-coupon bonds only?
Yes. In that case, each discount factor comes directly from price divided by face value. Coupon bonds are more informative when zero-coupon market quotes are unavailable.
4) What is the repriced column checking?
It recomputes each instrument price using the solved curve. A match between repriced value and input price confirms the recursive construction is internally consistent.
5) When should interpolation be used?
Use interpolation only when some earlier coupon dates fall between already solved nodes. It is a practical approximation, but strict exact-date solving is cleaner whenever the market set supports it.
6) Why are discount factors below one?
A discount factor converts future money into present money. Positive time value means one unit received later is worth less today, so discount factors usually remain below one.
7) What is the difference between spot and forward rates?
A spot rate discounts cash from today to one maturity. A forward rate describes the implied annualized rate between two future dates based on adjacent discount factors.
8) Can this support annual, semiannual, quarterly, or monthly coupons?
Yes. Each row includes its own coupon frequency. The maturity must still align with that frequency grid so the calculator can build valid coupon dates and recursive present values.