Volatility Term Structure Modeling

Volatility term structure modeling connects near-term events to long-term vol regimes—similar to yield-curve engineering but for variance expectations. Understanding how the term structure shifts enables calendar spread trades, dispersion strategies, and accurate pricing of products with multiple expiration dates.

Drivers of Term Structure Shape

Normal (upward-sloping):

• Near-term vol lower than long-term vol
• Markets calm, no imminent events
• Long-term uncertainty exceeds short-term

Inverted (downward-sloping):

• Near-term vol higher than long-term vol
• Crisis conditions or imminent event (earnings, election)
• Market expects stress to resolve

Flat:

• Volatility similar across tenors
• Transitional state between normal and inverted

Humped:

• Peak at intermediate tenor (e.g., 3-month)
• Scheduled event creates local vol spike
• Long-term mean reverts to normal

Modeling Techniques

Parametric Fits

• Power law: σ(T) = σ_∞ + (σ_0 - σ_∞) × T^(-α)
• Exponential decay: σ(T) = σ_∞ + (σ_0 - σ_∞) × e^(-λT)
• Nelson-Siegel style: σ(T) = β₀ + β₁e^(-T/τ) + β₂(T/τ)e^(-T/τ)

Parameters fit to observed ATM volatilities at each tenor.

Regime Shift Handling

When regime changes (e.g., crisis begins):

• Short-term vol spikes
• Long-term vol increases but less
• Curve inverts

Model can incorporate:

• Jump component for event risk
• State-dependent mean reversion
• Markov switching between regimes

Forward Variance

Forward variance σ²(t₁, t₂) is the implied variance for the period [t₁, t₂]:

σ²(t₁, t₂) = [σ²(0, t₂) × t₂ - σ²(0, t₁) × t₁] / (t₂ - t₁)

This decomposes term structure into period-by-period expectations.

Example:

• 1-month ATM vol: 22% → variance = 0.0484
• 3-month ATM vol: 20% → variance = 0.0400

1-3 month forward variance: = [0.0400 × 0.25 - 0.0484 × 0.0833] / (0.25 - 0.0833) = [0.0100 - 0.0040] / 0.1667 = 0.036

Forward vol (1M-3M) = √0.036 = 19%

The market implies lower volatility for months 2-3 than for month 1.

Calendar Spread Implications

Long calendar spread: Sell near-term vol, buy deferred vol

Profitable when:

• Term structure steepens (near-term vol falls, long-term rises)
• Near-term vol decays faster than long-term
• Event passes without moving long-term expectations

Short calendar spread: Buy near-term vol, sell deferred vol

Profitable when:

• Term structure flattens or inverts
• Near-term vol spikes
• Imminent event expected to drive short-term

Example trade: Current term structure:

• 1-month IV: 25%
• 3-month IV: 22%

Trade: Buy 1-month straddle, sell 3-month straddle (normalized by vega)

If 1-month vol spikes to 35% while 3-month stays at 23%:

• Gain on 1-month leg
• Small loss on 3-month leg
• Net profit from term structure move

Scenario: Term Structure Shift

Before Fed announcement:

Curve is inverted—high near-term uncertainty about Fed decision.

After Fed announcement (hawkish surprise):

Event resolution caused:

• Near-term vol to collapse (1-week: 30% → 22%)
• Curve to flatten/normalize
• Some long-term vol increase (3-month: 22% → 25%)

P/L for calendar trade: Long 1-month, short 3-month would have profited as 1-month fell 4 vols while 3-month rose 3 vols.

Dispersion and Correlation

Term structure also relates to dispersion:

• Index vol = function of single-stock vols and correlations
• When correlation rises, index vol increases relative to single-stock vol
• Dispersion trades benefit when realized correlation differs from implied

Term structure insight: If single-stock term structures are flat but index is inverted, implied correlation is elevated near-term—potential dispersion opportunity.

Sample Term Structure Data

Interpretation: Near-term vol elevated (Z-score +1.5), long-term closer to normal (+0.4). Event-driven inversion likely.

Next Steps

For understanding the smile dimension of volatility surfaces, see Implied Volatility Surface Basics.

To interpret skew signals, review Smile and Skew Interpretation.