Black-Scholes calculator with the Greeks
Every option price on your screen comes out of a formula like this one. Type in six numbers and see what a call and a put should cost — and exactly how fast each price moves when the stock, the clock or the volatility changes.
| Greek | Call | Put | What it means |
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How it works: the Black-Scholes model prices an option from six things: the stock price, the strike, the time left, how much the market expects the stock to swing (implied volatility), the interest rate and the dividend yield. It works out the odds of every possible stock price at expiry, then the average payout, pulled back to today's money. The Greeks are how fast that price changes when one input moves: delta for the stock, gamma for delta itself, theta for one day passing, vega for one point of volatility, rho for one point of interest rate. Prices are per share; one contract is 100 shares.
Why the call and put are tied together
Buy a call and sell a put at the same strike and date, and you get the same result as owning the stock. So the two prices can't drift apart: call minus put always equals the stock price minus the strike (both pulled back for interest and dividends). That rule is called put-call parity. It's why a high put price on a stock usually comes with a high call price too. For an option seller this matters in the wheel strategy: the put you sell and the covered call you sell later are priced off the same volatility.
Where the model is wrong
Black-Scholes assumes the stock moves smoothly and the swing size stays the same until expiry. Real stocks gap on earnings and news, and the market prices that in by charging more for far-out strikes. So the model is a shared language, not the truth. The input that moves the price most is implied volatility, and you read it from the market, not the model. See implied volatility explained and the Greeks explained.
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