Calculator Inputs
Use deposit rows for short maturities and bond rows for longer maturities. Bond price inputs are percentages of face value.
Example Data Table
This sample set is already loaded by default and produces a smooth educational zero curve with deposit anchors and coupon-bond extensions.
| Label | Type | Maturity (Y) | Coupon % | Quote / Price | Frequency |
|---|---|---|---|---|---|
| 6M Deposit | Deposit | 0.50 | 0.00 | 4.80 | 2 |
| 12M Deposit | Deposit | 1.00 | 0.00 | 5.10 | 2 |
| 18M Bond | Bond | 1.50 | 5.40 | 100.20 | 2 |
| 24M Bond | Bond | 2.00 | 5.65 | 100.55 | 2 |
| 30M Bond | Bond | 2.50 | 5.90 | 100.85 | 2 |
| 36M Bond | Bond | 3.00 | 6.10 | 101.10 | 2 |
Formula Used
DF(T) = 1 / (1 + r × T)
Here, r is the annual simple deposit rate and T is maturity in years.
Price = Face × (Quoted Price % / 100)
Bond price inputs are interpreted as percentages of face value.
Price = Σ[Coupon Cash Flow × DF(t_k)] + (Face + Final Coupon) × DF(T)
DF(T) = (Price - Σ earlier coupon PVs) / (Face + Final Coupon)
Earlier coupon present values use already solved discount factors or the selected interpolation rule.
z(T) = -ln(DF(T)) / T
z_m(T) = m × ((1 / DF(T))^(1 / (m × T)) - 1)
m is the number of compounding periods per year.
f(T1,T2) = ln(DF(T1) / DF(T2)) / (T2 - T1)
How to Use This Calculator
- Enter a face value, output convention, and coupon-date handling rule.
- Add deposit rows for short maturities where quoted market rates are available.
- Add bond rows for longer maturities using coupon rate, maturity, price, and frequency.
- Keep maturities unique and aligned with coupon frequency for cleaner results.
- Click Bootstrap Zero Curve to solve discount factors sequentially.
- Review the result table, repricing checks, and the Plotly term-structure chart.
- Use the CSV or PDF buttons to export your completed results.
Frequently Asked Questions
1) What is bootstrapping in a zero curve?
Bootstrapping derives zero rates sequentially from market instruments. Short maturities usually come from deposits, then coupon bonds extend the curve. Each newly solved discount factor prices the next instrument after subtracting earlier coupon cash flows discounted with previously solved nodes.
2) How is a zero curve different from a yield curve?
A zero curve shows one discount rate for each maturity with a single payment. A yield curve may describe par yields, coupon bond yields, or other quoted market rates. Bootstrapping converts mixed market quotes into consistent spot rates and discount factors.
3) Why are discount factors important?
Discount factors translate future cash flows into present value. If a payment of 100 arrives at time T, its present value equals 100 multiplied by DF(T). Bootstrapping solves DF(T) first, then converts that factor into a zero rate.
4) Why does coupon frequency matter?
Coupon frequency controls how many cash flow dates a bond contributes. Semiannual bonds create half-year coupon dates, quarterly bonds create quarter-year dates. More coupon dates generally require more earlier curve information or a reasonable interpolation method.
5) Are bond prices treated as clean or dirty?
This calculator treats bond prices as clean prices observed on a coupon date, so accrued interest is assumed zero. If your market quote includes accrued interest, use the dirty price instead or adjust the input before bootstrapping.
6) What does interpolation do here?
Interpolation estimates discount factors at coupon dates missing from exact earlier maturities. Log-linear interpolation on discount factors is common because it preserves positive discounting behavior. Strict mode avoids interpolation and requires coupon dates to match previously solved nodes exactly.
7) What are forward rates used for?
Forward rates are implied future short rates derived from discount factors between two maturities. They help analyze the curve’s shape, expected financing costs, and reinvestment assumptions. The calculator reports continuous forward rates between consecutive solved zero-curve points.
8) What are the main limitations?
The model is educational and practical, but it still relies on assumptions. Settlement timing, day-count rules, holiday calendars, compounding conventions, and off-cycle coupons can change professional pricing. Validate important results against your desk conventions and market data.