Volatility Cone & Realized Vol Lab
Construct multi-horizon volatility cones across 10-day to 252-day windows. Benchmark current implied volatility against historical percentile distributions and evaluate extreme-value realized estimators.
Multi-Horizon Volatility Envelopes
Market Presets:
Cone & Estimator Settings
Current IV vs Cone
84th %ile
Historically Rich
Volatility Risk Premium
+4.8%
IV > RV Premium
Estimator Efficiency
1.0x
Close-to-Close
Trade Strategy Bias
Sell Vol
Credit / Short Vega
Historical percentile dispersion bands (Max, 75th, Median, 25th, Min) with current Implied Volatility overlaid.
Historical density of realized volatility for the selected horizon with current IV position.
Statistical variance efficiency relative to Close-to-Close (Parkinson: 5x, Garman-Klass: 8x, Yang-Zhang: 14x).
Volatility Cone Percentile Matrix Across Horizons
| Horizon (Trading Days) | Minimum Vol (%) | 25th Percentile (%) | Median Vol (50th %) | 75th Percentile (%) | Maximum Vol (%) | Dispersion Span (Max - Min) |
|---|
Sensitivity: Vol of Vol ($\xi$) vs. Horizon on 75th %ile Vol (%)
Sensitivity: Current IV vs. Mean Vol on Vol Risk Premium (%)
Institutional Theory: Volatility Cones & Realized Estimators
1. Mechanics of the Volatility Cone
First popularized by Burghardt and Lane (1990), a Volatility Cone solves the critical problem of comparing option implied volatilities across different maturities. Because realized volatility over short intervals (10-20 days) experiences sharp transient spikes and crashes, its distribution is wide. As the measurement interval widens to 180 or 252 days, volatility mean-reverts toward its long-term average, creating a narrowing cone envelope.
2. Identifying Relative Value Opportunities
By mapping the implied volatility of options expiring in $T$ days directly into the cone:
- IV > 75th Percentile: Options are rich relative to historical distribution. Traders favor short vega, iron condors, calendar ratio spreads, or selling strangles.
- IV < 25th Percentile: Options are cheap. Traders favor long gamma, long straddles, or backspreads.
- 25th to 75th Percentile: Options are fairly priced; trade directional delta or skew rather than pure volatility levels.
3. Extreme-Value Realized Estimators
Standard Close-to-Close realized volatility wastes massive information contained in intraday highs and lows:
Parkinson (1980): Uses High ($H$) and Low ($L$) prices; 5x more statistically efficient than close-to-close:
$$\sigma_P^2 = \frac{1}{4 \ln 2 \cdot N} \sum_{i=1}^N \left(\ln \frac{H_i}{L_i}\right)^2$$
Garman-Klass (1980): Incorporates Open, High, Low, and Close; 8x more efficient:
$$\sigma_{GK}^2 = \frac{1}{N} \sum \left[ 0.5 \left(\ln \frac{H_i}{L_i}\right)^2 - (2\ln 2 - 1)\left(\ln \frac{C_i}{O_i}\right)^2 \right]$$
Yang-Zhang (2000): Independent of continuous drift and overnight opening jumps; 14x more efficient.
Volatility Cone & Estimators Mastery Quiz
1. Why does the volatility cone narrow as the rolling time horizon lengthens?
2. What trading action is indicated when 30-day IV trades above the 75th percentile of its cone?
3. What is the main statistical flaw of traditional close-to-close realized volatility?
4. What makes the Yang-Zhang volatility estimator exceptionally powerful?
Related Volatility & Derivatives Simulators
Frequently Asked Questions
A Volatility Cone is a financial chart that plots the historical distribution of realized volatility across various rolling time horizons (e.g., 10, 20, 30, 60, 90, 180, and 252 trading days). The resulting envelope forms a cone shape because short-term volatility exhibits extreme dispersion (wide opening), while long-term volatility mean-reverts toward the historical average (narrow tip).
Traders overlay current Implied Volatility (IV) term structures onto the historical cone. If current IV is near or above the 75th/Max percentile band, options are historically expensive (favoring credit spreads or vega shorting). If IV is near or below the 25th/Min band, options are historically cheap (favoring long gamma, straddles, or calendar spreads).
Standard close-to-close volatility only samples end-of-day prices, ignoring intraday price paths and requiring large sample sizes. Yang-Zhang combines overnight jump volatility, continuous open-to-close price dynamics, and Rogers-Satchell intraday range drift-independence. It is up to 14 times more efficient than close-to-close volatility.
The Volatility Risk Premium (VRP) is the structural tendency of implied volatility to trade at a premium over subsequently realized volatility. It represents the insurance markup investors pay market makers for tail risk protection.
Due to mean reversion and the central limit theorem, short-term shocks (earnings, geopolitical events) dissipate over longer sampling periods. A 10-day realized volatility can easily spike to 80% or drop to 5%, but a 252-day annual realized volatility naturally clusters around the long-term baseline.