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Read the direction of conversion
D(0,T) converts one unit due at T into its present value. When D exceeds one, a positive future payment has a larger present amount under that factor. The word discount does not impose D below one in every rate environment.
Recover the effective rate
For D(0,2) = 1.02, the two-year annual effective zero rate is 1.02^(−1/2) − 1, approximately −0.985246%. Accumulation over both years is 1/1.02. The rate must remain above −100% under this effective compounding convention.
| Quantity | Illustrative value | Meaning |
|---|---|---|
| Factor | 1.02 | Positive present conversion |
| Future payment | 100 | Positive receipt |
| PV | 102 | Positive present amount |
| Annual effective zero | −0.985246% | Negative accumulation rate |
Check rather than automatically delete the point
Confirm dates, quotation basis and units before accepting the factor. A factor above one can be intended; a negative factor would be a different issue. A curve with increasing factors contains negative implied interval rates under the selected convention.
Keep market claims separate
The illustration supplies a mathematical factor, not a live security quotation. Real market arbitrage conclusions depend on available instruments, costs, collateral, funding and contractual details. Do not infer an executable strategy from the sign alone.