What Is the Variance Risk Premium?

What VRP Is

Take any 30-day call option, observe its IV at trade. Hold the option through expiration. Compute the realized vol of the underlying over that 30-day window. The difference IV minus realized vol is the variance risk premium for that single trade. Average it across thousands of trades, across hundreds of underlyings, across two decades of options data, and the average is consistently positive: implied vol exceeds realized vol by roughly 2-4 vol points on the SPX at the 30-day tenor.

VRP is sometimes expressed in variance terms (IV^2 - RV^2) rather than vol terms (IV - RV) for analytical cleanness because variance is what is actually priced through option payoffs. The two metrics tell the same story but variance VRP scales differently than vol VRP.

Why VRP Exists

Three structural reasons option sellers demand and receive a positive premium for bearing variance:

• Variance shocks are correlated with bad market states. Volatility spikes when markets crash. Selling options is a position that loses money exactly when the rest of an investor's portfolio is also losing money. Bearing this correlated risk requires compensation, and the compensation shows up as IV exceeding RV in expectation.
• Jump risk and tail risk. The empirical distribution of underlying returns has fatter tails than log-normal. Option sellers are exposed to the jump-tail risk; they price it into IV but the realized frequency of jumps is lower in any individual sample window. Over long samples the realized jump frequency catches up but the priced premium persists because investors are risk-averse to the jump distribution itself, not just its mean.
• Demand for portfolio insurance. Institutional investors holding long equity buy puts as insurance. The persistent demand for downside insurance bids put-side IV up, fattens the priced left tail, and creates the structural premium that systematic short-vol strategies harvest.

Worked Example

SPX 30-day VRP measurement. Trailing 5-year average:

• Average 30-day IV: 16.2%
• Average 30-day subsequent realized vol: 13.4%
• Average VRP: 2.8 vol points (positive)
• Hit rate (% of months where IV exceeded subsequent RV): 73%

The 73% hit rate is the reason short-vol strategies generate positive alpha on average. They lose 27% of the time, often catastrophically (March 2020 short-vol losses were 5-10x typical monthly P&L). The premium is not free: it is compensation for bearing the variance-shock tail risk.

How Each Pricing Model Treats VRP

• Black-Scholes: a single-vol model. VRP is not internal to BSM; it is the empirical gap between BSM-implied IV (at trade) and BSM-realized vol (at expiration). BSM has no mechanism for the gap to be persistent because BSM has no risk premium structure - the gap is purely empirical.
• Heston: the variance-process drift parameter under Q vs P (kappa*theta in each measure) decomposes VRP cleanly. The risk-neutral drift toward long-run variance theta_Q exceeds the real-world drift toward theta_P because investors demand a premium for variance risk. Bates (Heston + jumps) extends this to decompose jump-tail premium separately.
• Jump diffusion: the priced jump intensity (lambda_Q) typically exceeds the realized jump intensity (lambda_P). This jump-risk premium is part of VRP. Decomposing total VRP into diffusive-vol premium plus jump-tail premium requires Bates or SVCJ models.
• SABR: per-expiration calibration; VRP shows up as the difference between calibrated alpha (vol level under Q) and subsequently realized vol over the option's life.

Term-Structure of VRP

VRP is not constant across tenors. The empirical pattern:

• 30-day VRP: the standard reference. ~2-4 vol points on SPX historically.
• 60-90 day VRP: slightly larger in volatility points and in variance points. Capturing more horizons of jump risk.
• 1-7 day VRP: smaller and more variable. Short-tenor IV is dominated by upcoming-event jump premium; in event-free windows, short-tenor VRP can be near zero or negative.
• 180-day+ VRP: typically larger in vol points, smaller in variance points (because vol is averaged over more diverse regimes). Long-tenor variance-swap rates are persistently above realized variance.

The term structure of VRP is itself a tradable signal. When near-tenor VRP collapses while long-tenor VRP holds, the market is paying down jump-tail premium without unwinding diffusion-vol premium. That divergence is informative about regime.

How to Measure VRP

• Variance swap rate vs realized variance. The cleanest measurement. The 30-day variance swap rate is the fair value of a contract paying realized variance over 30 days; comparing it to subsequently realized variance gives VRP directly. CBOE VIX-squared is approximately the 30-day SPX variance swap rate, though VIX has known skew-related biases.
• ATM IV vs RV. The standard retail measurement. Less clean than variance-swap-based measurement because ATM IV is sensitive to skew shape and not a pure variance metric.
• Equity hedge fund returns regressed on VRP. Provides indirect VRP measurement through the alpha contribution to short-vol portfolios.

When VRP Compresses

VRP is not constant. Three regimes where it compresses (and short-vol strategies underperform):

• After volatility spikes. When IV is already elevated, the gap between IV and realized vol narrows because realized vol catches up to elevated IV. Selling vol after a major drawdown produces negative VRP for the next 30-90 days while realized vol mean-reverts.
• During regime transitions. When the underlying regime changes (e.g., low-vol to high-vol), realized vol can persistently exceed prior-month IV. VRP turns negative until IV adjusts.
• Single-name event windows. Pre-earnings IV pricing is high because the event premium is real. Post-earnings, the next month's IV is low because the event premium has expired. VRP measured at single-name granularity has very different dynamics than index VRP.

Related Concepts

IV vs HV History · IV Crush · Term Structure · Tail Risk · Risk-Neutral Density · Expected Move · Pricing Model Landscape · Options Market-Structure Ontology

References & Further Reading

• Bollerslev, T., Tauchen, G., and Zhou, H. (2009). "Expected Stock Returns and Variance Risk Premia." Review of Financial Studies, 22(11), 4463-4492. The canonical VRP reference.
• Carr, P. and Wu, L. (2009). "Variance Risk Premiums." Review of Financial Studies, 22(3), 1311-1341. Cross-asset and term-structure decomposition of VRP.
• Drechsler, I. and Yaron, A. (2011). "What's Vol Got to Do with It." Review of Financial Studies, 24(1), 1-45. Equilibrium model of VRP and the equity premium.
• Bondarenko, O. (2014). "Why Are Put Options So Expensive?" Quarterly Journal of Finance, 4(03), 1450015. Decomposition of put-side VRP into tail and skew components.

View live SPY IV vs realized vol history ->

This page is part of the Pricing Model Landscape and the canonical reference set on options market structure. Browse all documentation.