Common Probability Distributions in Finance › Common Probability Distributions in Finance

Probability distributions are a core modeling tool in quantitative finance. Many portfolio-risk estimates, option-pricing models, and default-likelihood models require assumptions about how uncertain outcomes are distributed. A misspecified distribution can materially change estimated tail probabilities, option values, and risk limits.

The choice becomes especially visible in the tails. Later in this chapter, the same simulated heavy-tailed sample produces a lower 95% VaR but higher expected shortfall and higher 99% risk measures than a fitted normal model. That mixed result is the practical reason to inspect a distribution's assumptions rather than relying on a blanket rule about normal models.

This chapter covers several common models in quantitative finance: the normal distribution as a baseline for returns and mean-variance analysis, the lognormal distribution for positive quantities such as modeled asset prices, discrete distributions like the binomial and Poisson for counts and event models, and heavier-tailed alternatives. Whether any of them fits a particular dataset or decision well must be checked against the relevant horizon and evidence. For each distribution, we examine both the mathematical properties and the financial intuition behind its use.