Understanding Volatility
What is Volatility?
Volatility is a statistical measure that quantifies the dispersion of a dataset over time. In financial markets, it represents:
- The dispersion of asset returns
- An abstracted metric of the likely range for time series data points
- The magnitude of price changes within a stock's time series
Key Properties
- Bounded: Volatility can only be positive [0, ∞)
- Dynamic: Not a constant metric
- Globally: Stationary
- Locally: Non-stationary
- Multiple market volatility profiles relate to macroeconomic trends
- Constantly changing variation
- Usually expressed as unitless or percentage values
Types of Volatility
1. Implied Volatility (IV)
- Forward-projecting, used in options pricing
- Calculated using Black-Scholes model
- VIX: 30-day IV calculated from SPY call + put prices
- Creates a reflexive feedback loop with option prices
2. Historical Volatility (HV)
- Most commonly used metric
- Based on past performance
- Typically uses close-to-close prices
- Standard Deviation (σ) is the simplest metric
8 Ways to Calculate Volatility
- Standard Deviation (σ)
- Simple calculation
- Classic close-to-close HV metric
- Easy bias correction
- Effective for basic movement understanding
- Beta
- Simple calculation
- Useful for benchmarking against market
- Good for relative comparisons
- Squared Returns
- Simple calculation
- Easy bias correction
- Provides clear timeframe insights
- Parkinson
- Uses High + Low prices
- Best for Geometric Brownian Motion (5x better than close-close)
- Limitations: Misses close-to-open jumps and underlying trends
- Garman-Klass
- Uses OHLC prices
- 8x better than close-close for GBM
- Limitations: Similar to Parkinson
- Hodges-Tompkins
- Uses overlapping close-to-close prices
- Bias-corrected estimation
- Good for GBM applications
- Rogers-Satchell
- Uses OHLC prices
- Captures intraday movements and trends
- Handles price jumps within sessions
- Limitation: Can underestimate between-session volatility
- Yang-Zhang
- Most comprehensive (OHLC + overnight movements)
- 14x better than close-close for GBM
- Captures price jumps and trends
- Limitation: Jump events can dominate calculations
Choosing the Right Volatility Estimator
- No single "best" estimator exists
- Consistency in usage is crucial
- Consider your analysis timeframe
- Multiple estimators can provide better insights
- Real market data tends to show high correlation between different estimators
Why Use Volatility Analysis?
- Helps understand complex market dynamics
- Transforms chaos into measurable trends
- Quantifies risk tolerance
- Guides investment decisions:
- Position sizing
- Hedging strategies
- Trade timing
- Relative performance analysis
Practical Applications
- Match your investment horizon with appropriate estimators
- Use multiple estimators for comprehensive analysis
- Apply to any time series or financial metric
- Adapt calculations based on specific needs (overnight jumps, intraday movements, etc.)
References
- E. Sinclair, Volatility Trading, John Wiley & Sons, 2008
- Journal of Derivatives
- PyQuant News: "How to Compute Volatility: 6 Ways"