Volatility & advanced strategies
How does the assumption of a log-normal distribution fail to map true financial asset price tails?
By Easy Money Scanner · Educational reference · Not investment advice
The short answer
Black-Scholes assumes log-normal returns, implying thinner tails than observed in real markets, which tend to show more frequent extreme moves (fat tails) than the model predicts, especially during crises.
How it works
This mismatch is a key reason implied volatility smiles and skews exist in traded option prices, as the market prices extra premium into tail-risk strikes beyond what the lognormal model would suggest.
An example
During the 2008 financial crisis, realized market moves far exceeded what a lognormal distribution calibrated to pre-crisis volatility would have predicted, illustrating fat-tail risk.
Risk & limitations
Relying solely on lognormal-based models for risk management can understate the probability and magnitude of extreme losses, particularly for short volatility positions.
Examples are hypothetical, not trade recommendations. US contract and regulatory references do not automatically apply in Canada. Rules, margin requirements and broker policies can change; confirm them with the relevant authority and your broker.