Lognormal Distribution

Share prices, property values and many other financial quantities cannot fall below zero but can, in principle, rise without limit. A normal distribution, which allows negative values and is symmetrical, does not fit them well. The lognormal distribution does.

If a share's continuously compounded returns are normally distributed, its future price is lognormally distributed. This creates a distribution with a long right tail: most outcomes are moderate, but a few very large increases are possible, while losses are limited to the amount invested.

For example, a share priced at 100 might have a small chance of rising to 300 in a few years, while the most it can fall is to zero. Its possible future prices form a lopsided shape rather than a symmetrical bell.

The lognormal distribution is a key assumption in the Black–Scholes option pricing model and many other financial models. It is a useful approximation, but real asset prices often show fatter tails and sudden jumps that it does not fully capture.