Stock Option Calculator
A call or put option's intrinsic value and Black-Scholes price, with dividends, its Greeks, the break-even price at expiry and the profit or loss chart.
Result…
How it's calculated
d₁ = (ln(S ÷ K) + (r − q + σ² ÷ 2)T) ÷ (σ√T), d₂ = d₁ − σ√T Call = S·e^(−qT)·N(d₁) − K·e^(−rT)·N(d₂) Put = K·e^(−rT)·N(−d₂) − S·e^(−qT)·N(−d₁) Delta = e^(−qT)N(d₁) (call), e^(−qT)(N(d₁) − 1) (put); Gamma = e^(−qT)φ(d₁) ÷ (Sσ√T) Vega = S·e^(−qT)φ(d₁)√T ÷ 100; Theta and rho as in Hull, per day (÷ 365) and per 1% Break-even: call K + premium, put K − premium
An option gives the right, not the duty, to buy (a call) or sell (a put) a share at the strike price. Its intrinsic value is what it would be worth if exercised now; the rest of its price is time value, which shrinks to nothing by expiry. The Black-Scholes-Merton model prices a European option from the share price, strike, time left, volatility, the risk-free rate and a continuous dividend yield. The Greeks say how the price moves: delta per 1 unit of share price, gamma the change in delta, theta per calendar day, vega per 1 percentage point of volatility and rho per 1 point of interest rate. The break-even and the chart show the buyer's profit or loss at expiry for the premium paid. The model is a standard reference, not a forecast.
Your numbers, step by step
About the Stock Option calculator
This stock option calculator values a call or a put with the Black-Scholes-Merton model, including a continuous dividend yield. Enter the share price, the strike, the days to expiry, the volatility, the risk-free rate and the dividend yield, and it gives the model price, the intrinsic value and time value, the break-even price at expiry and the price of the matching option on the other side. Switch to “Greeks” for delta, gamma, theta per day, vega per 1% of volatility and rho per 1% of interest rate. A chart shows the buyer's profit or loss at expiry and today across a range of share prices. Each step, from d₁ and d₂ to the final price, is shown with your numbers, and the results were checked against independently computed Black-Scholes values. It is a learning and checking tool, not a forecast or advice.
How to use it
- Choose “Call” or “Put”, and “Value and break-even” or “Greeks”.
- Enter the “Share price now”, the “Strike price” and the “Days to expiry”.
- Enter the “Volatility”, the “Risk-free rate” and the “Dividend yield” as yearly percentages.
- Optionally enter the “Premium paid” for your own break-even and profit chart, then read the price and the Greeks.
Worked example
A call with a strike of 155 on a share at 150, 60 days to expiry, 30% volatility, a 4% risk-free rate and a 1% dividend yield is worth 5.44 per share by Black-Scholes. It has no intrinsic value, so all 5.44 is time value, and the break-even at expiry is 155 + 5.44 = 160.44. The put with the same strike is worth 9.67. Its Greeks: delta 0.4325, gamma 0.0215, theta −0.0644 a day, vega 0.2388 per 1 point of volatility and rho 0.0977 per 1 point of interest rate.
Updated
Questions people ask
How do I calculate the value of a stock option?
The intrinsic value is the share price minus the strike for a call, or the strike minus the share price for a put, and never below zero. A model such as Black-Scholes adds the time value from the volatility, the time left, interest rates and dividends.
What is the Black-Scholes formula for a call option?
Call = S × e^(−qT) × N(d₁) − K × e^(−rT) × N(d₂), where N is the standard normal distribution and d₁ and d₂ depend on the share price, strike, volatility, time and rates. The put follows from the same terms.
What do delta, gamma, theta, vega and rho mean?
Delta is how much the option price moves for a 1 unit move in the share. Gamma is how fast delta changes. Theta is the value lost per day, vega the change for 1 point of volatility, and rho the change for 1 point of interest rate.
How do I find the break-even price of an option at expiry?
For a call, add the premium paid to the strike; for a put, subtract it. Above a call's break-even, or below a put's, the buyer makes a profit at expiry, before fees. To size a share trade by the loss you accept, see the position size calculator.
Why is the market price different from the Black-Scholes value?
The model assumes a European option, constant volatility and rates, and no trading costs. Real options are often American, the market's implied volatility differs from the one you enter, and prices include a spread. Options carry a high risk of loss, so speak to a licensed financial professional before trading them.