The Volatility Risk Premium

The volatility risk premium describes compensation associated with bearing volatility risk. In empirical work, authors often compare option-implied volatility or variance with a forecast of future realized volatility or variance. Definitions and signs vary, so the first step is to identify exactly what is being measured.

Variance and volatility are different units

Using an implied-minus-realized convention, 25% implied volatility and 20% subsequently realized volatility produce a five-percentage-point ex-post gap. Their annualized variances differ by 0.25² − 0.20² = 0.0225. That variance difference is not “2.25 volatility points,” and neither difference is itself a dollar trading return.

An ex-ante risk premium compares risk-neutral pricing with an estimate of physical expected outcomes. An ex-post gap uses the outcome that actually occurred. One realized period can deviate sharply from an expectation even when the original estimate was reasonable.

Why compensation can exist

Protection can be especially valuable in adverse states when liquidity is scarce and investors want cash. Selling that protection exposes the seller to losses in those same states. Historical research published by Cboe on option benchmarks studies implied-versus-subsequent-realized gaps; its sample findings are not a rule that every contract is overpriced.

The observed gap depends on the market, dates, maturity, strike coverage and estimator. Demand for protection is a possible economic explanation, not something established simply by seeing one high IV quote.

Connect the statistic to a strategy

Selling a put combines downside price exposure with short volatility. Selling a straddle adds substantial movement risk in both directions. Delta hedging changes the exposure but introduces repeated trading, costs and discrete hedge error. A variance-linked instrument has different weighting again. These are not interchangeable implementations of the same return.

For example, a $100-strike put sold for $3 loses $1,700 per standard contract if the stock finishes at $80: $300 premium minus $2,000 intrinsic payout. A quiet price history before that drop offers no contractual protection. Margin calls can occur before expiration.

Evaluate compensation after the difficult parts

Include bid–ask costs, financing, collateral returns where relevant, hedge transactions, jumps and realistic sizing. Compare returns with drawdowns and capital tied up, not only premium collected. Test periods of stress separately from calm samples.

A persistent historical average can disappear for a chosen strike, horizon or implementation. The useful question is whether the proposed exposure offers adequate compensation under defensible assumptions and after costs. It is not whether “IV usually exceeds realized,” treated as a guarantee of a profitable next trade.