Black-Scholes Calculator
The model price for a call and a put at the same strike, side by side, with delta, gamma, theta, vega and rho for each — and the parity identity you can check by hand.
| Greek | Call | Put | What it measures |
|---|---|---|---|
| Delta | 0.533 | -0.467 | Price change per $1 in the stock |
| Gamma | 0.0555 | 0.0555 | Delta change per $1 in the stock |
| Theta | -0.053 | -0.042 | Value lost per calendar day |
| Vega | 0.114 | 0.114 | Price change per 1 point of IV |
| Rho | 0.041 | -0.041 | Price change per 1 point of rates |
Check it yourself: put-call parity says the call minus the put must equal the stock price minus the discounted strike. Here $3.02 − $2.69 = $0.33, and $0.33 the other way. They agree because the same model produced both — which is exactly why an arbitrage-free price for one right fixes the price of the other.
Greeks are per share; multiply by 100 for one contract. Theta is per calendar day, vega and rho per one percentage point. No dividend yield is applied — see the notes below for when that matters.
Black-Scholes calculator, explained
What is the Black-Scholes formula actually doing?
It answers one question: what would it cost to manufacture this option’s payoff by continuously trading the stock? If you can replicate the payoff exactly, the option cannot trade for more or less than the replication costs without leaving free money on the table, so the model price is an arbitrage argument rather than a forecast. That is also why implied volatility is the only input you cannot look up — everything else is observable, so the market price and the formula together tell you what volatility the market is assuming.
Why show a call and a put together?
Because they are not independent. Put-call parity fixes the price of one given the other, and seeing both makes the constraint visible — the calculator prints the check so you can verify it rather than take it on faith. It is also the fastest way to spot a data-entry mistake: if the two columns do not satisfy parity, an input is wrong.
Does it handle dividends? And American exercise?
No to both, deliberately. There is no dividend-yield input because our pipeline does not publish a forward-adjusted yield per name, and a field nobody can populate honestly is worse than no field. For short-dated options on non-dividend-paying names the difference is immaterial. Around an ex-dividend date on a high-yield name it is not, and neither is early exercise: American options can be worth more than this model says, most notably ITM calls just before a dividend and deep ITM puts. Treat the output as the European lower bound.
What units are the greeks in?
Per share, so multiply by 100 for one contract. Theta is per calendar day rather than annualised, and vega and rho are per one percentage point rather than per unit — those are the trading conventions, not the textbook ones, which is why a textbook vega looks 100× larger than ours.
The model assumes constant volatility. Does that break it?
It bends it, and the market has already priced around the problem. Real chains show a skew — different strikes trade at different implied volatilities, which is the market’s way of saying returns are not lognormal and crashes are fatter than the model allows. Use the strike’s own implied volatility as the input rather than one number for the whole chain, and Black-Scholes becomes a quoting convention that works rather than a theory that is wrong.
Where do I get a real volatility number to put in?
Every ticker has an IV rank page showing current implied volatility against its own 52-week range, which is the context that tells you whether the number you are about to type is high or low for that name. For the payoff rather than the price, use the options profit calculator, which needs no model at all.
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Educational, not investment advice. These are standard models applied to the numbers you enter — they describe what the maths implies, not what the market will do.