Student's t Distribution

A fat-tailed distribution that better models extreme market events.

The Student's t distribution has heavier tails than the normal distribution, making extreme events more likely. It's characterized by degrees of freedom (df): lower df means fatter tails. At df=3-5, tail events are 2-3x more likely than normal. As df increases, the t-distribution approaches normal. It's widely used in finance to model realistic return distributions and stress scenarios.

Formula

f(t) = \frac{\Gamma\left(\frac{\nu+1}{2}\right)}{\sqrt{\nu\pi}\,\Gamma\left(\frac{\nu}{2}\right)} \left(1 + \frac{t^2}{\nu}\right)^{-\frac{\nu+1}{2}}

Related Terms

Kurtosis (Excess)

Measures fat tails — how often extreme events occur vs. normal distribution.

Monte Carlo Simulation

Generating thousands of possible future scenarios through random sampling.

Value at Risk (VaR)

The maximum expected loss at a given confidence level — but doesn't tell you how bad the tail is.