Volatility: Implied vs Realised and the Variance Risk Premium

An option's price is mostly a bet on how much the underlying will move. The market states that bet as implied volatility, the volatility that makes a pricing model return the option's price. What later happens is realised volatility, the annualised standard deviation of the underlying's returns over the option's life. For US equity indices, implied has been higher than realised most of the time. Option sellers collect the gap, the variance risk premium (VRP), and give it back in bursts when markets fall. The academic evidence for the premium is strong. Peter Carr and Liuren Wu ("Variance Risk Premiums", Review of Financial Studies 22(3), 2009) built synthetic variance-swap rates from option prices and found strongly negative variance risk premiums on five stock indices and 35 individual stocks. That means buyers of variance paid more, on average, than variance later delivered. Bollerslev, Tauchen and Zhou ("Expected Stock Returns and Variance Risk Premia", RFS 22(11), 2009) showed that the gap between implied and realised variance predicted quarterly US stock returns over 1990–2007. The crash risk is just as well documented. The Cboe Volatility Index, the VIX, closed at a record 82.69 on 16 Mar 2020, and its intraday record is 89.53 on 24 Oct 2008 (Cboe data as reported by CNBC and others). On 5 Feb 2018 the VIX rose ~116% in a day (37.32 vs 17.31, +115.6% close to close), still its largest one-day percentage rise in Cboe's series to Nov 2026. Credit Suisse's inverse-VIX note XIV lost ~94.5% ($5.99 redemption vs $108.3681) after hours and was terminated (Shared facts). On 5 Aug 2024 the VIX reached ~65–66 before the US open, which the BIS called its biggest one-day spike, and closed near 38 (BIS Bulletin 95; SEC DERA working paper; reported). Volatility has also become a traded asset class. VIX options averaged a record ~862,000 contracts a day in 2025, up from ~830,000 in 2024 (Cboe full-year volume release, Jan 2026). Exchange-traded products let retail accounts go long or short VIX futures in a brokerage account, and the long products have lost most of their value over every multi-year period they have existed (section 7). This section defines the volatilities, explains the VIX and its futures curve, sets out the evidence for the VRP and how big it is, shows why long-volatility products decay and short-volatility products blow up, and covers skew, dispersion and correlation premia. The companion worked example computes the roll yield of VIX futures and the decay of a stylized long-VIX product over a calm year.