Black-Scholes Model
A theoretical pricing framework under stated assumptions—not a guaranteed fair price or complete model of real option markets.
The Black-Scholes-Merton framework values European-style options under assumptions including specified price dynamics, continuous trading and hedging, frictionless markets, and model inputs such as volatility and rates. Variants can incorporate continuous dividend yield, but real markets exhibit jumps, smiles, skew, discrete dividends, early exercise, costs, and liquidity constraints.
Frequently Asked Questions
Does Black-Scholes produce the true option price?
No. It produces a model value conditional on inputs and assumptions. Market prices can differ because of volatility surfaces, supply and demand, funding, borrow, dividends, jumps, transaction costs, liquidity, and model risk.
Does the basic model ignore dividends?
The original non-dividend form does, while common extensions include a continuous dividend yield. Discrete dividends and early-exercise features may require other methods.
Can Black-Scholes value American options?
The standard closed-form formula is for European-style exercise. American options, especially dividend-paying calls and puts, may require binomial, finite-difference, simulation, or other numerical methods.
What does implied volatility represent in the model?
It is the volatility input that reconciles a market option price with the chosen model and other inputs. Different strikes and maturities generally imply different volatilities, producing a surface rather than one universal number.