Volatility Term Structure

The normal state of the volatility term structure where longer-dated options trade at higher implied volatilities than shorter-dated ones.

• Reflects the volatility risk premium demanded by sellers for bearing uncertainty over longer horizons
• Typical in calm, trending equity markets where near-term realized volatility is low
• Creates a positive roll yield for short VIX futures positions as contracts converge downward toward spot
• Example: VIX at 15 with 2-month futures at 17 and 4-month futures at 19

An inverted term structure where near-term implied volatility exceeds longer-dated volatility, signaling immediate market distress.

• Occurs during crisis events, earnings shocks, or geopolitical turmoil when front-month uncertainty spikes
• Reflects the market's expectation that current elevated volatility is transitory and will mean-revert
• Creates a negative roll yield for long VIX futures positions as contracts converge upward toward spot
• Example: VIX at 35 with 2-month futures at 28 and 4-month futures at 24

Localized convexity in the term structure where implied volatility spikes for expirations surrounding a known future event.

• Common around earnings announcements, FDA drug approvals, elections, or central bank decisions
• The spike reflects the market pricing in a binary outcome with a discrete jump risk on a specific date
• Decays rapidly after the event passes, creating term structure arbitrage opportunities via calendar spreads
• Traders isolate the event premium by buying the pre-event expiration and selling the post-event expiration

The term structure exhibits a strong gravitational pull toward a long-run equilibrium level, reflecting the mean-reverting nature of volatility itself.

• Short-dated volatility is more elastic and responsive to spot moves, while long-dated volatility is sticky
• The speed of mean reversion is a critical parameter in stochastic volatility models like the Heston model
• After volatility spikes, the term structure typically flattens and returns to contango as fear subsides
• This property underpins volatility selling and risk premium harvesting strategies

The carry earned or paid when maintaining a position in VIX futures or options across expirations as contracts roll along the term structure.

• Positive roll yield (contango): Short futures positions gain as contracts decline toward spot VIX
• Negative roll yield (backwardation): Long futures positions lose as contracts rise toward spot VIX
• The magnitude depends on the steepness of the term structure slope between the front and second month
• Example: Rolling a short position from 17 to 15 yields +2 points of decay capture per cycle

The spread between long-dated and short-dated implied volatility can be decomposed into distinct risk components.

• Volatility risk premium: Compensation for bearing unhedgeable stochastic volatility risk over time
• Jump risk premium: Additional premium for the possibility of discontinuous price gaps
• Event risk premium: Specific premium for scheduled binary outcomes clustered at certain expirations
• Liquidity premium: Compensation for the wider bid-ask spreads and lower depth in longer-dated options
• Understanding this decomposition enables relative value trading across the term structure

The foundational three-dimensional plot of implied volatility across varying strike prices and expiration dates. The term structure is a single slice of this surface, isolating the time dimension. A complete, arbitrage-free surface is essential for pricing path-dependent exotic derivatives and requires strict adherence to no-arbitrage conditions to prevent butterfly and calendar spread violations.

These terms describe the slope of the term structure, particularly in VIX futures. Contango is the normal, upward-sloping state where longer-dated futures trade at a premium, reflecting a volatility risk premium. Backwardation is an inverted, downward-sloping curve that typically occurs during market stress or panic, indicating an expectation that current high volatility will subside.

A class of models, including the Heston Model, where volatility itself follows a random process rather than remaining constant. These models are crucial for accurately capturing the term structure because they introduce a volatility of volatility parameter that controls the convexity of the forward volatility curve and the kurtosis of the return distribution.

The quantitative process of fitting a parametric or non-parametric model to market-quoted option prices to construct a smooth, arbitrage-free surface. Effective calibration ensures the model's term structure perfectly matches liquid market instruments. Techniques like the Dupire Equation derive a unique local volatility surface, while the SABR Model captures the dynamics of the smile for a single maturity.

A dimensionality reduction technique that decomposes historical volatility surface movements into orthogonal components. The first three factors typically explain over 95% of the variance:

• Parallel Shift: The overall level of the term structure moves up or down.
• Slope (Twist): Short-dated volatility moves inversely to long-dated volatility.
• Curvature (Butterfly): The belly of the term structure moves relative to the short and long ends.

A forward contract on future realized variance that provides a pure play on the term structure of volatility without delta risk. The spread between the variance swap rate and the implied volatility of a corresponding option defines the volatility risk premium. The term structure of variance swaps is a direct, model-free measure of the market's expectation of future variance at different horizons.