Volatility Risk Premium (VRP) is the compensation associated with bearing volatility risk that is embedded in option prices. In formal variance-based treatments, it is commonly measured as the difference between the market's risk-neutral expectation of future return variance, inferred from option prices, and the corresponding physical or statistical expectation of variance. In practical research, the term is also often used for the tendency of option-implied variance to exceed the variance subsequently realized by the underlying asset. Those two ideas are closely related, but they are not identical.
Expected premium versus realized outcome
The formal premium is an ex-ante concept: it compares two expectations formed before the future variance is known. The risk-neutral expectation reflects option pricing under the market's pricing measure, while the physical expectation describes the statistically expected variance under real-world probabilities. Because the latter is not directly observable, empirical work frequently estimates VRP using option-implied variance minus the variance subsequently realized over the same horizon.
That substitution creates an important interpretation boundary. The resulting implied-minus-realized measure is partly an ex-post outcome. An unexpectedly large volatility shock can push realized variance above the level previously implied by options, producing a negative realized premium for that period even when investors ordinarily require compensation to bear volatility risk.
Why measurement choices matter
VRP is usually most precise when expressed in variance rather than volatility units. Variance is volatility squared, so subtracting two quoted volatility percentages is not mathematically equivalent to subtracting their variances. Formal model-free implied-variance measures can also use option prices across a broad range of strikes rather than relying on one at-the-money implied-volatility observation. Expiration horizon, realized-variance sampling frequency, annualization convention and option-surface construction can therefore materially change the measured premium.
Positive option-implied-versus-expected or realized variance spreads have been widely documented in equity-index markets and are consistent with investors paying to transfer volatility and tail risk while counterparties require compensation for accepting that exposure. The premium is nevertheless time-varying and can become negative over particular realized periods. It should therefore be interpreted as a priced risk relationship, not as proof that options are mechanically overpriced, a guaranteed return from selling volatility or a directional forecast for the underlying market.