How Does the Assumption of a Lognormal Distribution of Stock Prices Affect the Model’s Accuracy?

The assumption of a lognormal distribution implies that stock price movements are random and normally distributed, which is a cornerstone of the Black-Scholes model. However, in reality, financial markets often exhibit "fat tails," meaning extreme price movements occur more frequently than a normal distribution would predict.

This discrepancy can lead to the model underpricing the risk of deep out-of-the-money options, which would pay off during these extreme events. Consequently, the model may not accurately reflect the true probability of significant market swings, affecting its pricing accuracy for certain options.