Black-Scholes Calculator
Calculate black-scholes from your own entered figures.
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Currency: Amounts are calculated in the currency you select; this site does not convert between currencies and does not use live exchange rates.
What this tool does
Calculate black-scholes from your own entered figures. European options on a non-dividend-paying underlying with constant volatility and risk-free rate; market option prices also reflect dividends, early exercise and supply/demand.
How to use the Black-Scholes Calculator
- Enter or select underlying price (s).
- Enter or select strike price (k).
- Enter or select time to expiry (years).
- Enter or select risk-free rate (%).
- Enter or select volatility (%).
- Read the calculated result; change any measurement to compare alternatives.
Formula
d1 = (ln(S/K) + (r + σ²/2)T)/(σ√T), d2 = d1 − σ√T; call = S·N(d1) − K·e^(−rT)·N(d2); put = K·e^(−rT)·N(−d2) − S·N(−d1); N() is the standard normal CDF (Abramowitz–Stegun erf approximation)
- spot
- Underlying price (S)
- strike
- Strike price (K)
- years
- Time to expiry (years)
- rate
- Risk-free rate (%)
- vol
- Volatility (%)
European options on a non-dividend-paying underlying with constant volatility and risk-free rate; market option prices also reflect dividends, early exercise and supply/demand.
Worked example
For black-scholes calculator, the following measurements illustrate the exact method: Underlying price (S): 100; Strike price (K): 100; Time to expiry (years): 1; Risk-free rate (%): 5; Volatility (%): 20.
Inputs
- Underlying price (S)100
- Strike price (K)100
- Time to expiry (years)1
- Risk-free rate (%)5
- Volatility (%)20
Result
- Call option price$10.45
- Put option price$5.57
- Call delta0.64
- Put delta-0.36
- Gamma0.02
- Vega (per 1% volatility change)0.38
Results explained
- Call option price
- Call option price from the formula above. European options on a non-dividend-paying underlying with constant volatility and risk-free rate; market option prices also reflect dividends, early exercise and supply/demand.
- Put option price
- Put option price from the formula above. European options on a non-dividend-paying underlying with constant volatility and risk-free rate; market option prices also reflect dividends, early exercise and supply/demand.
- Call delta
- Call delta from the formula above. European options on a non-dividend-paying underlying with constant volatility and risk-free rate; market option prices also reflect dividends, early exercise and supply/demand.
- Put delta
- Put delta from the formula above. European options on a non-dividend-paying underlying with constant volatility and risk-free rate; market option prices also reflect dividends, early exercise and supply/demand.
- Gamma
- Gamma from the formula above. European options on a non-dividend-paying underlying with constant volatility and risk-free rate; market option prices also reflect dividends, early exercise and supply/demand.
- Vega (per 1% volatility change)
- Vega (per 1% volatility change) from the formula above. European options on a non-dividend-paying underlying with constant volatility and risk-free rate; market option prices also reflect dividends, early exercise and supply/demand.
Frequently asked questions
d1 = (ln(S/K) + (r + σ²/2)T)/(σ√T), d2 = d1 − σ√T; call = S·N(d1) − K·e^(−rT)·N(d2); put = K·e^(−rT)·N(−d2) − S·N(−d1); N() is the standard normal CDF (Abramowitz–Stegun erf approximation)
European options on a non-dividend-paying underlying with constant volatility and risk-free rate; market option prices also reflect dividends, early exercise and supply/demand.
No. All numbers are entered by you or come from the dated reference table shown on this page; calculations run locally.
This is an estimate, not financial, tax or legal advice. Verify the inputs and output with official sources and a qualified professional.
Check period consistency, currency, percentage inputs and the assumptions: European options on a non-dividend-paying underlying with constant volatility and risk-free rate; market option prices also reflect dividends, early exercise and supply/demand.