Price call and put options using the Black-Scholes model. Calculate premium, Greeks (delta, gamma, theta, vega), break-even price, and P/L at expiry.
Options give you the right — but not the obligation — to buy (call) or sell (put) an underlying asset at a specified price before a certain date. The Black-Scholes model is the foundational framework for pricing European-style options, and it remains widely used across finance.
This calculator prices both call and put options using the Black-Scholes formula, accounting for the underlying price, strike price, time to expiry, volatility, risk-free rate, and dividend yield. It computes the key Greeks — delta, gamma, theta, vega, and rho — which measure the option's sensitivity to various factors.
The profit/loss table shows your potential outcomes at expiry across a range of stock prices, helping you make informed decisions about whether an option trade fits your risk/reward profile. Preset scenarios for common trades let you quickly explore how different setups behave.
Use the preset examples to load common values instantly, or type in custom inputs to see results in real time. The output updates as you type, making it practical to compare different scenarios without resetting the page.
Use this to estimate a theoretical option premium and see how price, volatility, time, rates, and dividends affect the contract. It also surfaces the Greeks, which are useful for understanding directional exposure and time decay.
Call = S₀·e^(-qT)·N(d₁) − K·e^(-rT)·N(d₂) Put = K·e^(-rT)·N(−d₂) − S₀·e^(-qT)·N(−d₁) d₁ = [ln(S/K) + (r − q + σ²/2)T] / (σ√T) d₂ = d₁ − σ√T Where S = spot, K = strike, T = time, r = risk-free rate, σ = volatility, q = dividend yield.
Result: Premium ≈ $3.25
A call option with strike $180 on a $175 stock with 30 days to expiry and 25% IV is priced around $3.25. The break-even stock price at expiry is $183.25. Delta of ~0.38 means the option gains about $0.38 for every $1 stock increase.
The Black-Scholes model provides a standard benchmark for European-style option pricing. This calculator uses the main contract inputs to estimate premium and Greeks, then shows the break-even level and expiry profit or loss across a range of stock prices.
Match the expiration format, volatility estimate, and dividend yield to the contract you are pricing. Option values are especially sensitive to implied volatility and time remaining, so use live market inputs when you want a tradeable comparison.
The output is a theoretical price, not a guaranteed market quote. Actual premiums can differ because of bid-ask spread, early-exercise features, and volatility skew.
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This worksheet prices a European-style call or put with the Black-Scholes model using the spot price, strike, time to expiry, implied volatility, risk-free rate, and dividend yield shown on the page. The premium is computed from the standard Black-Scholes formula, while delta, gamma, theta, vega, and rho are estimated numerically from small changes in the underlying inputs rather than from closed-form Greek formulas.
The profit-and-loss table is an expiry payoff view built from the model premium, not a path-dependent options simulation. The page is intended as a theoretical benchmark for European-style contracts, so American early-exercise value, bid-ask spread, skew, and liquidity effects are outside the model.
Delta measures how much the option price changes for a $1 move in the underlying. A delta of 0.50 means the option gains $0.50 when the stock rises $1.
Theta is time decay — the amount of value the option loses each day. Option sellers benefit from theta; buyers fight against it.
IV is the market's expectation of future volatility priced into the option. Higher IV means more expensive options.
Black-Scholes is designed for European options. American options (which can be exercised early) may be worth slightly more, especially puts.
For calls: strike + premium. For puts: strike − premium. The stock must pass this level at expiry for you to profit.
It provides a solid theoretical baseline, but real option prices deviate because of volatility skew, dividends, liquidity, and early-exercise features. It is most useful as a benchmark, not as a perfect market quote.