Black-Scholes model

The classic formula for pricing an option from the stock price, strike, time, interest rate and volatility — the basis for the Greeks.

The Black-Scholes model is a formula that estimates the fair price of a European option based on a few inputs: the stock price, the strike, the time left until expiration, the risk-free interest rate, and how volatile the stock is expected to be. Instead of guessing what an option should cost, it gives you a theoretical number to compare against the market price.

In practice, most traders never solve the equation by hand. Their broker or charting software already runs it in the background to display the Greeks, so you use it indirectly every time you check the delta, theta, or vega of a position. If a call is trading well above its Black-Scholes value, the market may simply be pricing in more expected volatility than the model assumes.

The classic mistake is treating the output as a guaranteed price. The model assumes constant volatility and ignores dividends and early exercise, which is why American options and real markets often deviate from it. Traders effectively feed volatility in, so the number is only as good as the volatility estimate you put behind it.

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