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Options Premium (Black Scholes) Calculator

Work out options premium (black scholes) instantly with clear inputs, formula shown and shareable results.

About Options Premium (Black Scholes) Calculator

Black-Scholes prices an option as the discounted expected payoff under a lognormal price distribution, using a 6% risk-free rate here. The premium splits into intrinsic value — what it is worth exercised now — and time value, which decays to zero at expiry.

Formula

Black-Scholes

C = S·N(d₁) - Ke^(-rT)·N(d₂), d₁ = [ln(S/K) + (r + σ²/2)T]/(σ√T)

S
Spot
K
Strike
σ
Volatility
T
Years

Worked example

With the default values below, Options Premium (Black Scholes) Calculator returns Call Option Premium of $18.5165. Change any input above and every figure here is recalculated in your browser.

Inputs used

Spot Priceminimum 0
1,000
Strike Priceminimum 0
1,050
Implied Volatilityaccepts 1–300 %
25 %
Days To Expiryaccepts 1–1,095
45

Results

Call Option Premium
$18.5165
Put Option Premium
$60.7780
Intrinsic Value Of The Call
$0.0000
Time Value Of The Call
$18.5165

Step by step

  1. 1Values used
  2. 2Black-Scholes
  3. 3Call Option Premium= 18.5165
  4. 4Put Option Premium= 60.7780
  5. 5Intrinsic Value Of The Call= 0.0000
  6. 6Time Value Of The Call= 18.5165

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
  • Figures are estimates for planning only. Market returns are not guaranteed, and rates, limits and tax rules change. This is not financial or tax advice — speak to a qualified adviser before acting.
  • This is an estimate for general information and not professional financial, tax or legal advice. See the full disclaimer for the limits that apply to this kind of calculator.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Figures are estimates for planning only. Market returns are not guaranteed, and rates, limits and tax rules change. This is not financial or tax advice — speak to a qualified adviser before acting.

Frequently Asked Questions

Why is volatility the key input?

It is the only input not directly observable, and the premium is highly sensitive to it — which is why options are quoted in volatility terms.

What are the model's main limitations?

It assumes constant volatility, no jumps and continuous hedging. Real markets violate all three, hence the volatility smile.

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