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

1. Standard Deviation (σ)
   • Simple calculation
   • Classic close-to-close HV metric
   • Easy bias correction
   • Effective for basic movement understanding
2. Beta
   • Simple calculation
   • Useful for benchmarking against market
   • Good for relative comparisons
3. Squared Returns
   • Simple calculation
   • Easy bias correction
   • Provides clear timeframe insights
4. Parkinson
   • Uses High + Low prices
   • Best for Geometric Brownian Motion (5x better than close-close)
   • Limitations: Misses close-to-open jumps and underlying trends
5. Garman-Klass
   • Uses OHLC prices
   • 8x better than close-close for GBM
   • Limitations: Similar to Parkinson
6. Hodges-Tompkins
   • Uses overlapping close-to-close prices
   • Bias-corrected estimation
   • Good for GBM applications
7. Rogers-Satchell
   • Uses OHLC prices
   • Captures intraday movements and trends
   • Handles price jumps within sessions
   • Limitation: Can underestimate between-session volatility
8. 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"