What Is the Key Limitation of the Black-Scholes Model?

The key limitation of the Black-Scholes model is its underlying assumptions, which often do not hold true in real-world markets. Specifically, it assumes that volatility is constant, asset prices follow a log-normal distribution, and continuous trading is possible without transaction costs.

In reality, volatility changes, asset returns exhibit 'fat tails' (more extreme events), and trading is discrete with costs. These limitations lead to the model underpricing deep out-of-the-money and in-the-money options.