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Keep the base payment schedule fixed
Use receipts 5, 5, 105 and annual spots 4%, 5%, 6%. Base value is 97.502864. In the scenario, the year-two spot rises to 8%, while the year-one and year-three spots remain explicitly unchanged.
Reprice the affected date only
The year-two PV changes from 5/1.05² = 4.535147 to 5/1.08² = 4.286694. The two other payment PVs are unchanged under this specified map. Total scenario value is 97.254411.
| Date | Spot-rate change | PV change |
|---|---|---|
| Year one | 4% → 4% | 0 |
| Year two | 5% → 8% | -0.248453 |
| Year three | 6% → 6% | 0 |
Expect implied forwards to adjust
Recovering one-year forwards from the altered spot curve can change both adjacent forward intervals. That does not mean the year-three cumulative factor must change: the forward products reconcile back to the supplied unchanged three-year spot factor.
Avoid calling this a full key-rate model
The demonstration uses independent dated spot nodes and payments at those exact dates. A practical key-rate shock usually includes a specified interpolation profile and broader exposures. State that profile before applying the result to an actual portfolio.