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Set the underlying pricing condition
For original current price 100, terminal prices 130 and 80 and factor 1.05, solve q×130+(1−q)×80=105. The two state weights sum to one, and the interior setup gives both positive.
Isolate the higher-state weight
The equation becomes 50q+80=105, so q=0.5. The lower-state weight is also 0.5. This is derived from prices and the period factor, not supplied as a historical frequency or subjective view.
Weight and discount the claim
The call pays 30 or zero. Its weighted expiry amount is 15, then its current value is 15/1.05=14.285714. Weighting and discounting are separate operations.
| Step | Amount |
|---|---|
| Weighted underlying expiry | 105 |
| Weighted call payoff | 15 |
| Current call value | 14.285714 |
Do not relabel a weight as a prediction
The weights support this no-arbitrage pricing model. They do not show a 50% observed chance that an actual underlying reaches 130. A real-world probability estimate answers another question.