Black-Scholes Calculator
Price European call and put options with the Black-Scholes model and see the Greeks.
About the Black-Scholes Calculator
The Black-Scholes(-Merton) model values a European option from the stock price, strike, time to expiry, volatility, risk-free rate and dividend yield. It assumes constant volatility and log-normal prices, so real option prices differ, especially far from the money; American options that can be exercised early (and pay dividends) are worth at least as much. The Greeks show sensitivity to each input.
The formula
C = S e^(−qT) N(d₁) − K e^(−rT) N(d₂); d₁ = [ln(S/K) + (r − q + σ²/2)T] ÷ σ√T; d₂ = d₁ − σ√T
Worked example
Example: Call / put value = $3.18 / $11.88
- Inputs: Stock price: $110; Strike price: $120; Days to expiry: 99 days; Volatility (annual): 28%; Risk-free rate: 4%; Dividend yield: 0%.
- Formula: C = S e^(−qT) N(d₁) − K e^(−rT) N(d₂); d₁ = [ln(S/K) + (r − q + σ²/2)T] ÷ σ√T; d₂ = d₁ − σ√T
- Result: Call / put value = $3.18 / $11.88
Questions people ask
What volatility should I use?
The option's implied volatility from your broker, or historical volatility as a rough guide.
Does put-call parity hold?
Yes: C − P = S e^(−qT) − K e^(−rT).