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Read this as an arithmetic stress case
The original hypothetical inputs are deliberately unusual: one long put, strike 100, premium 120. They are not presented as a plausible market quote. The purpose is to test the payoff tool’s boundary handling.
Calculate the largest holder payoff
For S≥0, max(100−S,0) cannot exceed 100. Therefore simple holder profit cannot exceed 100−120=−20. A positive premium above the maximum terminal payout cannot be recovered under this unfinanced model.
Reject a negative-price breakeven
The algebraic candidate K−premium is −20, outside the selected nonnegative terminal-price domain. The tool should omit a valid-domain boundary rather than report −20 as an attainable underlying price.
| Terminal price | Holder payoff | Simple profit |
|---|---|---|
| 0 | 100 | -20 |
| 50 | 50 | -70 |
| 100 | 0 | -120 |
| 150 | 0 | -120 |
Keep the stress test separate from current valuation
No pricing consistency or present-value claim is made for the supplied premium. Assessing whether a real quote violates a price bound requires exercise, discounting, income and other contract assumptions.