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A call gives its buyer the right to buy the underlying at the strike. Expiry intrinsic value is max(S−K, 0); profit also deducts premium and costs.

A put gives its buyer the right to sell at the strike. A falling stock does not guarantee profit: entry premium, time and IV also matter.

Intrinsic value is max(S−K,0) for calls and max(K−S,0) for puts. Premium minus intrinsic value is extrinsic value, which reflects more than time alone.

The local change in theoretical option value for a $1 underlying move. Position Delta includes direction, quantities and multiplier; it is not a probability of profit.

The rate at which Delta changes with the underlying price. High Gamma means directional exposure changes quickly; a static Delta cannot describe a large move.

The local effect of calendar time passing with other inputs fixed. This site uses per-day units. Not every position has negative Theta.

The local option-value change for a one-percentage-point change in IV. Position values here include the contract multiplier; actual changes are not guaranteed.

Delta sensitivity to volatility, equivalently Vega sensitivity to the underlying price. Always specify whether volatility is measured in decimals or percentage points.

The change in Delta as time passes, with other inputs fixed. Time direction and annual versus daily conventions differ between sources.

Near-strike expiry creates uncertainty about exercise or assignment. After-hours moves can leave unintended stock exposure beyond a spread payoff diagram.

An option seller is required to fulfill the contract. American-style options can be assigned early, and spread legs are not guaranteed to be processed together.

A sharp drop in implied volatility. A long option can lose despite a favorable stock move when falling IV and time decay outweigh the directional gain.

Annualized volatility inferred from an option price under a chosen model. It is not a promise of realized volatility or a directional forecast.

Dispersion of past returns. The lab annualizes sample standard deviation of daily log returns by sqrt(252); use consecutive adjusted daily closes.

Here: (current IV−sample minimum)/(sample maximum−sample minimum)×100. Undefined for a flat history; it can be outside 0–100 when current IV is outside the supplied sample.

Here: the percentage of historical observations strictly below current IV. Use comparable tenor and measurement conventions; tie handling changes results.

IV varies across strikes for one expiry. Both wings may sit above at-the-money IV, producing a smile; actual shapes vary by market and date.

Asymmetry across a same-tenor volatility curve, such as higher IV for lower-strike puts. Compare consistent tenor and Delta or moneyness.

The relationship between IV across expiries at comparable moneyness. Events can lift near-term IV above longer tenors; the curve is not a guaranteed forecast.

The lab uses S×IV×sqrt(calendar days/365) as a one-standard-deviation dollar approximation. It is not a maximum move or a guaranteed probability interval.