01 Contract
Both calls and puts are priced from the same inputs. The selection below sets which contract leads the summary, the Greek grid and the read — the other side stays fully priced too.
02 Market inputs
The two price levels the contract references today.
03 Time to expiration
Enter it in years directly, or in calendar days — the tool converts between the two using 365 days per year.
04 Rates & volatility
Rates, volatility and dividend income are supplied as annual percentages and compounded continuously by the model.
05 Read
What the numbers mean for the selected contract.
Set spot, strike, time, rate and volatility to price the option.
The Black-Scholes-Merton model prices a European option from the risk-free discounting of its distribution of terminal payoffs, under the assumptions that the underlying follows a geometric Brownian motion with constant volatility and that you can hedge continuously without cost.
Both the call and the put are computed live as you type. Nothing you enter leaves this page.
06 Model & assumptions
The conditions the Black-Scholes-Merton price is built on. Read these before acting on any number.
- •Underlying price follows a log-normal distribution with constant volatility σ over the option's life — no fat tails by construction.
- •No jumps. The model cannot see gaps in the underlying; a real crash or spike is outside its distribution.
- •European exercise only. Exercise is allowed at expiration, not before — American-style early-exercise value is not captured.
- •Risk-free rate r and volatility σ are held constant for the whole life; dividends enter only as the continuous yield q you entered.
- •Positions are assumed continuously hedgeable with no transaction costs, taxes or borrow constraints.
- •Probability in the money is the risk-neutral probability N(d₂) — it assumes markets price at the risk-free rate, not the real-world drift.