Black-Scholes model.

In plain English

The Black-Scholes model is a formula that converts five inputs into a theoretical option price, assuming the stock drifts and wobbles in small continuous steps. Four of the five inputs are observable. The fifth, future volatility, is not, so traders often run the model backward: they take the market price and solve for the volatility that would produce it, which is called implied volatility. The model assumes constant volatility and no sudden jumps, and real markets supply both. That gap is why quoted prices form a volatility skew rather than a flat line across strikes.

01Why it matters

Almost every option quote, Greek, and risk screen a brokerage platform displays is built on this model or a close relative, so its assumptions shape the numbers on the screen.

02The math, step by step

Two calls on the same stock share a strike and differ only in time: one has 30 days left, one has 90. Feed both into the model with the same volatility and the 90 day call prices higher, because there is more time for the stock to travel. Tripling the time does not triple the price, since the model scales roughly with the square root of time.

Illustrative example. The amounts here are hypothetical, chosen to show how the math works, not real quoted rates or figures.

03What this is NOT

04Receipts

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