Black Scholes Calculator

Value a European option under declared Black–Scholes assumptions. Results are deterministic educational calculations—not financial, tax, legal or investment advice.

Calculate instantly

Result

Prepares a Chat draft with these inputs and this result. Nothing is shared with QELLY until you choose Send.

Worked example

The calculator opens with this registered example. Replace one assumption at a time to see how the deterministic result changes.

Example inputs

{
  "spot": 100,
  "strike": 105,
  "timeYears": 0.5,
  "riskFreeRatePercent": 5,
  "dividendYieldPercent": 0,
  "volatilityPercent": 25,
  "optionType": "call"
}

Example output

{
  "optionType": "call",
  "price": 5.988479701648,
  "callPrice": 5.988479701648,
  "putPrice": 8.396020464623,
  "delta": 0.481579682092,
  "gamma": 0.022543522919
}

Input glossary

Required inputs for this method: Spot, Strike, Time to expiry, Volatility, Option Type. Validation boundaries below come from the registered calculator schema.

Spot

Enter spot for this calculation.

Required · Unit: currency

Strike

Enter strike for this calculation.

Required · Unit: currency

Time to expiry

Enter time years for this calculation.

Required · Unit: years

Risk-free rate

Enter risk free rate percent for this calculation.

Optional · Unit: %

Dividend yield

Enter dividend yield percent for this calculation.

Optional · Unit: %

Volatility

Enter volatility percent for this calculation.

Required · Unit: % · Minimum: 0

Option Type

Enter option type for this calculation.

Required · Allowed: call, put

Assumptions and limits

Method: Black-Scholes European Option · version 1.0.0 · formula ID black-scholes.
The calculation uses only the values entered on this page; it does not silently fetch live market data.
Fees, taxes, liquidity, slippage and other costs are included only when the registered inputs explicitly model them.
Display locale and rounding can change presentation, not the underlying deterministic receipt.

Edge cases

Inputs outside registered validation rules return an error rather than a fabricated result.
Array, matrix or cash-flow fields must be valid JSON in the structure described by their input label.
Extreme assumptions can be mathematically valid but economically unrealistic; use them as sensitivity tests rather than forecasts.

Frequently asked questions

Does this calculator require an account?

No. It works publicly without login. Calculations run locally. Explain result prepares a local Chat draft; your inputs and result are shared with QELLY only if you choose Send.

Is the result a recommendation?

No. It is a deterministic formula receipt whose usefulness depends on the assumptions you enter.

Why can market outcomes differ?

Fees, taxes, liquidity, volatility, timing and future returns may differ from the model assumptions.

Can I share my inputs?

Yes. Share creates an optional URL fragment containing only the inputs you choose to share. The fragment is not sent to QELLY by the calculator page.