Monte Carlo VaR Underestimates Tail Risk: 3 Distribution Fixes

#montecarlo #valueatrisk #riskmanagement #studentst

Why Your Monte Carlo VaR Is Lying to You

Most risk managers run Monte Carlo VaR with a normal distribution and call it a day. Then 2008 happens.

The problem isn't Monte Carlo itself — it's the assumption that returns follow a Gaussian distribution with nice, thin tails. Real asset returns have fat tails, skewness, and kurtosis that make normal distributions look like children's fairy tales. When you simulate 10,000 portfolio paths using np.random.normal(), you're systematically underestimating the probability of catastrophic losses.

I'm going to show you three distribution fixes that actually capture tail risk: Student's t-distribution, Generalized Pareto Distribution (GPD) for extreme value modeling, and GARCH-based filtered returns. Each one addresses a different failure mode of the vanilla normal assumption, and I'll give you working Python code for all three.