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Convert the supplied rate
The factor is 0.95, which remains positive. Grown current price is 95, strictly between lower 80 and higher 110. A negative rate is not automatically an invalid model input.
Calculate the interior state weight
q=(95−80)/(110−80)=0.5. The call pays 10 in the higher state and zero in the lower, so weighted expiry amount is 5. Current value is 5/0.95=5.263158.
Check the replication
Δ=10/30=1/3. Terminal cash is −80/3, with current cash −80/(3×0.95). Adding its current value to underlying cost 100/3 gives the same 5.263158.
| Input/output | Value |
|---|---|
| Period factor | 0.95 |
| Grown current price | 95 |
| Higher pricing weight | 50% |
| Current call value | 5.263158 |
Retain the mathematical and practical boundaries
The case assumes common-rate frictionless financing and no underlying income. A factor that is zero or negative is outside this model. A valid arithmetic factor does not establish an actual available funding arrangement.