Futures & Market Research Glossary

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.

Volatility skew is the variation in implied volatility across option strikes for the same underlying asset and expiration, particularly an asymmetric difference between the lower- and higher-strike sides of the option surface. This distinguishes skew from a volatility smile: a smile describes curvature in which implied volatility is relatively high toward both wings compared with the middle of the strike range, while skew emphasizes an imbalance between the two sides. Because implied volatility is inferred from option prices rather than directly observed, both shapes describe how option pricing varies across the strike dimension rather than separate realized-volatility measurements.

Skew describes relative pricing, not a directional forecast

A common downside skew has lower-strike options trading at higher implied volatilities than higher-strike options. In equity-index options, this pattern is often associated with demand for downside protection and perceived downside-tail risk, while other markets or regimes can show flatter or upward-sloping relationships. Hedging demand, option supply, positioning, perceived tail exposure and other market-structure effects can all contribute. A steep downside skew therefore shows that downside option volatility is relatively rich; by itself, it does not prove that the underlying is expected to fall or reveal why the pricing difference exists.

There is no single universal skew number

“Skew” can describe the broader cross-strike asymmetry or a statistic constructed from selected parts of that pattern. One common approach compares the implied volatilities of an out-of-the-money put and call at matched absolute deltas, producing a risk-reversal measure. Other methods estimate asymmetry from a wider set of strikes or from separate measures of the put and call sides of the option surface. Those constructions can produce different values from the same market data.

For that reason, a reproducible skew series requires its convention to be specified. Expiration, strike, moneyness or delta coordinates, option selection, normalization and any interpolation or surface-construction method can affect the result. This also distinguishes volatility skew from volatility term structure: skew compares relative implied volatility across strikes within an expiration, whereas term structure compares volatility across expirations. Two markets can therefore have similar at-the-money implied volatility yet materially different pricing of their downside and upside wings—a difference that a single headline volatility number will not reveal.

Volatility term structure is the pattern of implied volatility across option expirations for the same underlying market. It shows how volatility embedded in option prices changes with time horizon: short-dated options may carry higher, lower or similar implied volatility than longer-dated options. A meaningful comparison normally keeps the strike dimension as consistent as practical—for example, by comparing at-the-money options or comparable deltas—because changing both expiration and moneyness can mix volatility term structure with volatility skew.

What the slope does—and does not say

The term structure is not simply a forecast line for future realized volatility. Implied volatility is inferred from option prices, so differences across expirations can reflect expected future variability, event risk, volatility-risk compensation and option-market supply and demand. A known event concentrated inside one expiration window can therefore create a local hump: an option expiring after the event may embed substantially more volatility than one expiring before it, while the same event can have a smaller annualized effect on much longer-dated options. During acute market stress, short-dated implied volatility can also rise much faster than longer-dated volatility, producing an inverted structure.

The deeper arithmetic is in variance

Quoted implied volatilities are annualized standard deviations, but volatility itself is not the quantity that adds through time. Under a consistent variance and moneyness convention, each maturity can instead be expressed as total implied variance, approximately proportional to implied volatility squared multiplied by time to expiration. The difference between two compatible total-variance horizons can then be used to infer the forward variance priced for the interval between them. Consequently, forward volatility between two maturities is not obtained by simply subtracting one quoted implied-volatility percentage from another. This distinction matters especially around event dates, where a relatively small difference in headline volatility can conceal a concentrated amount of variance in a short interval.

Term structure is not the VIX futures curve

An option-implied volatility term structure should also be distinguished from a curve of volatility-futures prices. The former compares volatility inferred from options across different expiration horizons; the latter compares futures contracts that settle to a volatility index on different dates. They are economically related but are not interchangeable measurements.

Volatility term structure is therefore useful for locating where the options market is concentrating volatility pricing through time. Its interpretation still depends on comparable strikes or deltas, consistent calculation conventions and awareness of event timing. A steep, flat or inverted curve describes the current relative pricing of volatility horizons; by itself, it does not determine what realized volatility will ultimately be.