On this page
Use one stated curve
Annual spot rates at years one, two and three are 4%, 5% and 6%. There is one positive payment of 100 at year three. The comparison changes the representation of the curve, not the payment or its timing.
Recover the interval factors
The first factor is 1.04. The year-one-to-two factor is 1.05²/1.04 = 1.060096. The year-two-to-three factor is 1.06³/1.05² = 1.080287. These are accumulation factors; subtract one to express the one-year forward rates.
Multiply and cancel the intermediate terms
Their product is 1.04 × (1.05²/1.04) × (1.06³/1.05²) = 1.06³. The denominators cancel their matching prior factors. This cancellation provides an independent structural check rather than simply adding three percentages.
| Description | Expression | PV |
|---|---|---|
| Spot | 100 / 1.06³ | 83.961928 |
| Forward product | 100 / (1.04 × f12 factor × f23 factor) | 83.961928 |
Distinguish a pricing identity from realization
The identity holds for forwards constructed from the supplied curve. It does not require a statement that actual future rates will equal these forwards. If independently entered forward rates fail the equality, inspect conventions and inputs before claiming they belong to the same curve.