Payoff Lab: Expiry Comparison
Why equal strikes can share a terminal shape while differing in entry value and path risk.
#Terminal shape versus time value
For the same strike and per-share premium, the simplified terminal formula has the same capped shape regardless of term. Market premiums differ because more time permits a wider range of price paths.
V_T = min(S_T, K) + P_T#Illustrative terms
| Dimension | 7-day example | 30-day example | 90-day example |
|---|---|---|---|
| Upside commitment | Short | Medium | Long |
| Reset frequency | High | Moderate | Low |
| Total time value | Generally lower | Generally intermediate | Generally higher |
| Near-expiry gamma | Can be concentrated | Less concentrated initially | Spread over a longer horizon |
| Event exposure | Fewer days | More days | Many more days |
#Annualization
Multiplying a seven-day premium by 52 assumes 52 comparable and executable resets without gaps, missed periods, changing volatility or a changed Stock Token price. That is a scenario, not a return observation.