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Start with an explicit instrument set
Use fictional same-basis prices: a one-year zero paying 100 costs 96; a two-year annual 5-coupon bond costs 99; a three-year annual 6-coupon bond costs 101. They are assumed to have compatible payment certainty and valuation dates. Mixed credit quality would not identify one common default-free curve.
Subtract the value of known earlier payments
The zero gives D1 = 0.96. The two-year instrument obeys 99 = 5D1 + 105D2, so subtract the first coupon’s value before dividing by 105. The denominator includes the final coupon as well as redemption.
Reuse the solved factors
D2 = 0.897143. The third instrument obeys 101 = 6D1 + 6D2 + 106D3. Solve D3 only after valuing both earlier coupons. A supplied market price is not divided by the final redemption alone.
| Instrument | Known contribution | Remaining equation |
|---|---|---|
| One-year zero | None | 96 = 100D1 |
| Two-year coupon | 5D1 | 99 − 5D1 = 105D2 |
| Three-year coupon | 6D1 + 6D2 | 101 − 6D1 − 6D2 = 106D3 |
Reprice the original instruments
Insert the solved factors back into every original price equation. Matching those prices checks the algebra. It does not establish an unobserved intermediate factor or prove that a chosen interpolation method is uniquely correct. Retain instrument dates and price conventions in the worksheet.