The volatility risk premium is the difference between the implied volatility priced into options and the volatility the underlying later realises. On equity indices, implied volatility has on average traded above subsequent realised volatility. The gap is the compensation option sellers receive for bearing large and sudden losses.
How it works
Buyers of options, especially index puts, pay for protection against crashes and for the convexity that comes with it. Sellers provide that insurance and demand a premium for it. The premium is measured as implied volatility minus the volatility realised over the same horizon, or in variance terms with variance swaps. It is not stable. It tends to be positive in calm periods and can turn sharply negative in a sell-off, when realised volatility jumps above the implied level paid a month earlier. The distribution of outcomes is therefore asymmetric: frequent small gains for the seller, rare large losses.
Example
Hypothetical: a trader sells a one-month variance swap at a strike of 20 with a vega notional of 40,000, so a variance notional of 40,000 / (2 × 20) = 1,000. If realised volatility comes out at 16, the seller gains 1,000 × (400 − 256) = 144,000. If it comes out at 30, the seller loses 1,000 × (900 − 400) = 500,000.
On the desk
Practitioners look at the premium net of tail events, not its average in quiet years. Position sizing and the cost of protecting the tail decide whether harvesting it survives a single bad month.
Educational definition. Worked examples are hypothetical. Not an offer or a recommendation.