Stock price changes are modeled with thin-tailed lognormal distributions, not fat-tailed ones

Evidence

In what became the standard model of changes in stocks’ prices, the statistical distribution of changes in the natural logarithms of stock prices is the normal distribution the canonical “bell-shaped” curve of statistical theory. This “lognormal” model is an example of what the mathematician and chaos theorist Benoit Mandelbrot calls “mild” randomness: the tails of the normal distribution, representing the probabilities of extreme events, are “thin.” In the 1960s, Mandelbrot put forward a different model: one in which the tails are so “fat” that the standard statistical measure of a distribution’s spread (the standard deviation or its square, the variance) is infinite. — Donald MacKenzie, An Engine, Not a Camera, 138

Categorization

• DEFINE: Defines the lognormal model, mild vs. wild randomness, and the concept of fat versus thin tails clearly.
• XREF: Connects to Mandelbrot’s broader work on fractals and the critique of normal distributions in finance, and to Taleb’s ‘Black Swan’ arguments. — connects to: The bell-curve shape of Gaussian distributions is what banks’ risk models assume; Mandelsbrot’s infinite-variance price model implies infinitely expected stock prices — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 517; Deliberately assuming wild randomness can paradoxically keep markets mild — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 1169 (+4 more)

Broader Connections

• Mandelsbrot’s infinite-variance price model implies infinitely expected stock prices #corroborates (0.85) — Donald MacKenzie, An Engine, Not a Camera, 517
• Deliberately assuming wild randomness can paradoxically keep markets mild #qualifies (0.75) — Donald MacKenzie, An Engine, Not a Camera, 1169