Vol Regimes

Vol regimes are persistent market states characterized by particular volatility levels and behaviors.

Definition

A vol regime is a period where volatility exhibits consistent characteristics:

• Level (high/low)
• Behavior (trending, mean-reverting, jumping)
• Dynamics (how it responds to spot moves)

Common Regimes

Regime	BTC IV Range	Characteristics
Low Vol	30-45%	Range-bound, grinding, low realized vol
Normal Vol	45-65%	Healthy trends, moderate swings
High Vol	65-90%	Fast moves, elevated fear
Crisis Vol	90%+	Panic, capitulation, gaps

Volatility Clustering

One of the most robust empirical findings: volatility clusters. High vol days follow high vol days; low follows low.

GARCH Representation

The standard model for vol clustering:

$$\sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2$$

Where:

• $\omega$ = Long-run variance contribution
• $\alpha$ = Shock impact (ARCH term)
• $\beta$ = Persistence (GARCH term)

High $\alpha + \beta$ (near 1) means high persistence.

GARCH(1,1) Properties:

Unconditional variance:

$$\sigma^2 = \frac{\omega}{1 - \alpha - \beta}$$

Half-life of vol shock:

$$t_{1/2} = \frac{\ln(0.5)}{\ln(\alpha + \beta)}$$

For typical equity parameters ($\alpha = 0.1$, $\beta = 0.85$), half-life is about 14 days.

Estimation: Usually via maximum likelihood on log-returns.

Mean Reversion

Despite clustering, vol tends to revert to long-term levels.

Speed of Reversion

Measured by the mean-reversion parameter $\kappa$:

$$d\sigma = \kappa(\bar{\sigma} - \sigma)dt + \text{noise}$$

Crypto vol reverts faster than equity vol (higher $\kappa$).

Implications

• Extreme vol readings don't persist
• After spikes, expect gradual decline
• After calm periods, expect eventual increase

Volatility Risk Premium (VRP)

The tendency for IV to exceed subsequent RV on average.

$$\text{VRP} = \mathbb{E}[\text{IV}] - \mathbb{E}[\text{RV}]$$

Historical VRP by Market

Market	Typical VRP	Notes
SPX	2-4 vol points	Very consistent
BTC	5-15 vol points	Higher and variable
ETH	5-20 vol points	Similar to BTC

VRP Dynamics

VRP varies by regime:

• Low vol: VRP compressed or negative
• Post-spike: VRP often very high
• Normal: Moderate positive VRP

Close-to-Close:

$$\sigma_{\text{CC}} = \sqrt{\frac{252}{n} \sum_{i=1}^{n} (\ln(C_i/C_{i-1}))^2}$$

Parkinson (High-Low):

$$\sigma_{\text{PK}} = \sqrt{\frac{252}{4n\ln(2)} \sum_{i=1}^{n} (\ln(H_i/L_i))^2}$$

Garman-Klass (OHLC):

$$\sigma_{\text{GK}} = \sqrt{\frac{252}{n} \sum_{i=1}^{n} \left[0.5(\ln(H_i/L_i))^2 - (2\ln(2)-1)(\ln(C_i/O_i))^2\right]}$$

Parkinson and Garman-Klass are more efficient estimators but sensitive to gaps.

Regime Detection

Simple Methods

1. Percentile ranking: Where is current IV vs history?
2. IV/RV ratio: Is IV rich or cheap?
3. Term structure shape: Backwardation suggests high near-term risk

Statistical Methods

1. Rolling statistics: 20-day realized vol percentile
2. Markov regime switching: Formal state estimation
3. Hidden Markov Models: Probabilistic regime identification

Trading in Different Regimes

Regime	Long Vol	Short Vol	Key Risk
Low Vol	Cheap but bleeds	Works but exposed to spikes	Sudden transition
Normal	Fair	Fair	No edge
High Vol	Expensive	Risky	Continued elevation
Crisis	Very expensive	Dangerous	Anything goes

See Also

• Reading Volatility: Vol Regimes Lesson
• Term Structure
• Vol Surface