The volatility risk premium (VRP) is the gap between what the options market prices in and what the underlying actually delivers. The formula fits in one line. The interesting part is in the inputs, the unit conversions, and a handful of mistakes that produce a plausible-looking but wrong number.

This post walks through the math, a worked SPY example, a self-contained Python implementation in 30 lines, and the five pitfalls I see in almost every homemade implementation.

TL;DR

VRP = sigma_IV - sigma_RV # vol units VRP_var = sigma_IV ** 2 - sigma_RV ** 2 # variance units

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Where:

sigma_IV is annualized implied vol (typically 30-day ATM IV)

sigma_RV is annualized realized vol over a matched window

If 30-day ATM IV is 18% and 30-day realized vol is 12%, VRP is +6 vol points. Positive on ~70 to 75% of trading days across major US equity indices over the last 30 years. That spread is the structural edge premium sellers harvest.

The formula is the easy part.…