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Black-Scholes Option Estimate

Quick answer

ATM call ≈ 0.4 × S × σ × √T: a 100 stock with 30% volatility over 6 months prices an at-the-money call near 8.5.

  • Results update as you type.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

How the Black-Scholes Estimate Calculator Calculates Results

C = S·N(d₁) − K·e^(−rT)·N(d₂), with d₁ = (ln(S/K) + (r + σ²/2)T) ÷ (σ√T)

The Black-Scholes model estimates a European option's fair value from five inputs: spot, strike, rate, volatility and time. The calculator also shows the at-the-money shortcut. Mathematically, the engine applies C = S·N(d₁) − K·e^(−rT)·N(d₂), with d₁ = (ln(S/K) + (r + σ²/2)T) ÷ (σ√T). For an at-the-money 6-month call on a 100 stock with 30% volatility and a 5% rate, Black-Scholes gives ≈8.7; the quick proxy 0.4 × 100 × 0.30 × √0.5 ≈ 8.5 lands within 3%. Everything you enter stays in your browser, and the answer appears in the same units as your inputs the moment the figures are complete.

  1. 1

    Step 1

    Fill in each input field with your own data.

  2. 2

    Step 2

    The tool runs the formula C = S·N(d₁) − K·e^(−rT)·N(d₂), with d₁ = (ln(S/K) + (r + σ²/2)T) ÷ (σ√T) on your figures.

  3. 3

    Step 3

    Review the result displayed on screen.

  4. 4

    Step 4

    Refine the inputs until the numbers fit your case.

Use Cases

Options education

Building intuition for the five Greeks-adjacent inputs

Fair-value sanity check

Comparing a quote against the model estimate

Volatility implied solving

Back out σ from a market price

Expiry planning

Seeing time decay's effect on value

Common Mistakes

  • Using historical vol blindly

  • Ignoring dividends

  • Treating the estimate as exact

FAQs

Why does volatility dominate the price?

Options gain from swings both ways: higher σ widens the payoff distribution — from 20% to 40% volatility roughly doubles this call to ≈16.

When does Black-Scholes misprice?

Early exercise (American puts), dividends before expiry, skew-smiling volatilities and gap risk — use it as an estimate, not gospel.

What is the math behind the Black-Scholes Estimate Calculator?

The Black-Scholes Estimate Calculator applies C = S·N(d₁) − K·e^(−rT)·N(d₂), with d₁ = (ln(S/K) + (r + σ²/2)T) ÷ (σ√T), where S spot, K strike, r rate, σ volatility, T years to expiry.

How do I know the result is right?

The Black-Scholes Estimate Calculator uses the standard closed-form formula shown above; the accuracy depends only on the figures you supply.

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