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Name the promised receipt vector
Take receipts 5 at year one, 5 at year two and 105 at year three. Each illustrative zero unit pays 100 at its named year and nothing at other dates. The replication concerns fixed promised receipts, with common payment certainty and no trading frictions.
Scale each zero payment
Buy 0.05 units of the year-one zero, 0.05 units of the year-two zero, and 1.05 units of the year-three zero. Their receipt vector is exactly 5, 5, 105. Matching total cash alone would not suffice if the dates differed.
| Zero maturity | Units | Payment per unit | Matched receipt |
|---|---|---|---|
| 1 year | 0.05 | 100 | 5 |
| 2 years | 0.05 | 100 | 5 |
| 3 years | 1.05 | 100 | 105 |
Add the scaled zero prices
If each zero price is 100Dt, the package price is 0.05×100D1 + 0.05×100D2 + 1.05×100D3 = 97.502864 under the 4%, 5%, 6% example curve. This is the same dated present-value expression as the coupon schedule.
Keep replication assumptions explicit
A price difference in a classroom frictionless model motivates a no-arbitrage check. A real trade needs instrument access, financing, short-sale permissions, settlement and costs. Also, a defaultable bond’s state-dependent payments are not automatically replicated by default-free zeros with matching face amounts.