Term Structure

Term structure describes how implied volatility changes across expiries. It tells you when the market expects risk to show up.

Definition

Term structure is the pattern of IV across time at a fixed strike (usually ATM). Is near-term vol higher or lower than far-term vol?

Key Points

• Contango (normal): Far-term IV > near-term IV - uncertainty accumulates over time
• Backwardation (inverted): Near-term IV > far-term IV - event risk is imminent
• Term structure changes constantly around events
• After events, expect vol crush and normalization

See It In Action

Term Structure

Backwardation: Near-term IV > far-term. Signals event risk priced in.

Toggle between shapes to see how term structure changes. Backwardation often signals an upcoming event.

The Two Main Shapes

Shape

What It Looks Like

What It Means

Example

Contango

7d: 45% → 30d: 50% → 90d: 55%

No near-term event. Uncertainty grows with time.

Calm market, no news

Backwardation

7d: 75% → 30d: 55% → 90d: 50%

Event risk priced NOW. Something is happening soon.

FOMC in 3 days, ETF decision

Why Backwardation = Event Risk

When you see near-term IV much higher than far-term:

1. The market expects a specific event to cause a move
2. That event is imminent (within the near-term expiry)
3. After the event, near-term IV will collapse (vol crush)
4. Far-term IV stays relatively stable (event doesn't affect long-term uncertainty)

Example: BTC 7-day IV at 85%, 30-day at 55%. That 30-point spread screams "something is happening this week." Check the calendar.

Event Pricing

Events are the primary driver of term structure shape.

Before the Event

• Options spanning the event trade at a premium
• Term structure inverts (backwardates) around the event date
• Near-term ATM vol spikes; far-term less affected

Event Type

Typical Term Structure Effect

How Long Before

FOMC / Rate Decision

Sharp backwardation 2-5 days out

1 week

Crypto Upgrade (e.g., ETH merge)

Backwardation builds for weeks

2-4 weeks

BTC Halving

Mild backwardation, elevated baseline

Months

ETF Decision

Extreme backwardation if date known

1-2 weeks

Earnings (stocks)

Classic overnight vol crush pattern

1 week

After the Event

• Vol crush: Near-term IV collapses (the event premium evaporates)
• Term structure normalizes to contango
• If you were long near-term options, you likely lost on vega even if direction was right

This is why trading pre-event is tricky. You need the move to be bigger than what's priced in.

Volatility Mean Reversion

Volatility doesn't stay high or low forever. It tends to revert to a long-term average.

The intuition:

• When current vol is high, the market expects it to come down (contango builds)
• When current vol is low, the market expects it to rise (mild backwardation or flat)

This creates a natural pull toward "normal" levels over time.

A simple mean-reverting vol term structure:

$$\sigma(T) = \sigma_\infty + (\sigma_0 - \sigma_\infty)e^{-\kappa T}$$

Where:

• $\sigma_\infty$ = Long-term average vol (where vol "wants" to be)
• $\sigma_0$ = Current spot vol
• $\kappa$ = Mean reversion speed (how fast it gets there)

Example: If current vol is 80% but long-term average is 50%:

• Near-term options price closer to 80%
• Far-term options price closer to 50%
• This creates natural contango

More sophisticated models (like GARCH) add volatility clustering, where high vol periods tend to persist before reverting.

Volatility Clustering

One of the most robust findings in finance: high vol days follow high vol days.

When you see elevated vol today, it's likely to stay elevated tomorrow. This is why:

• Panic doesn't end in one day
• Calm markets stay calm for extended periods
• Regime changes are sudden but regimes persist

GARCH (Generalized Autoregressive Conditional Heteroskedasticity) is a model that captures volatility clustering:

$$\sigma^2_t = \omega + \alpha \epsilon^2_{t-1} + \beta \sigma^2_{t-1}$$

In plain English: Tomorrow's volatility depends on:

• A baseline level ($\omega$)
• Today's surprise move ($\alpha \epsilon^2_{t-1}$)
• Today's volatility ($\beta \sigma^2_{t-1}$)

The $\alpha + \beta$ term determines persistence. Values close to 1 mean vol shocks persist a long time.

For traders, the takeaway is simple: don't assume vol will instantly normalize after a spike. It takes time.

The Volatility Risk Premium (VRP)

On average, implied vol exceeds realized vol. This is the volatility risk premium.

Why it exists:

• Option sellers demand compensation for bearing uncertainty
• Option buyers pay for insurance even if they never use it
• It's the "insurance premium" embedded in options

How big is it?

Market	Typical VRP
SPX	2-5% (IV - RV)
BTC	Variable, 5-15% in calm periods
Post-crisis	Very large (IV stays elevated, RV drops)

Trading implication:

• Selling options has a statistical edge (collecting VRP)
• But the edge is compensation for tail risk
• When tails hit, they hit hard

$$\text{VRP} = \text{IV} - \text{RV}$$

Or the variance risk premium:

$$\text{VRP}_\text{var} = \text{IV}^2 - \text{RV}^2$$

How to track it:

1. Record current ATM IV (e.g., 30-day)
2. Wait 30 days
3. Calculate realized vol over that period
4. VRP = the IV you saw minus the RV that happened

This is backward-looking. For forward-looking estimates, compare current IV to recent RV trends.

Forward Variance

The term structure lets you extract the market's expectation for vol during a specific future period.

Example: If 30-day IV is 50% and 60-day IV is 55%, what's the implied vol for days 30-60?

$$\sigma^2_{30 \to 60} = \frac{\sigma_{60}^2 \times 60 - \sigma_{30}^2 \times 30}{60 - 30}$$

If forward variance for a specific period is much higher than surrounding periods, there's likely an event in that window.

Forward variance must be non-negative. If it were negative, you could construct a calendar spread for free money (a violation of no-arbitrage principles).

This means:

$$\sigma_{T_2}^2 \times T_2 \geq \sigma_{T_1}^2 \times T_1 \quad \text{for } T_2 > T_1$$

Total variance must increase with time. This doesn't mean IV increases (variance = IV² × time), but it constrains how much IV can drop at longer expiries.

Trading Term Structure

Strategy	What You Do	When to Use
Long Calendar	Sell near-term, buy far-term	Expecting near-term vol to crush
Short Calendar	Buy near-term, sell far-term	Expecting near-term vol to spike
Diagonal	Calendar at different strikes	Term structure view + directional view

Calendar spreads are bets on term structure shape changes.

Crypto Term Structure Patterns

Feature	Description
Higher baseline	Even "flat" crypto term structure is at 40-60% IV
Faster normalization	Post-event, crypto term structure snaps back quickly
Event-heavy	Frequent forks, upgrades, regulatory news create regular inversions
Correlated	Alt term structures tend to follow BTC's lead

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Related:

• Vol Surface - The complete picture
• Skew - The strike dimension
• Vol Regimes - High vs low vol environments
• Reading Volatility: Term Structure Lesson - Full course lesson