Parkinson Volatility: More Accurate Volatility from High-Low Range Data

Parkinson Volatility estimates annualized volatility using the high-low range of each bar instead of close-to-close changes. It captures intraday price movement that close prices completely miss — making it statistically more efficient than standard Historical Volatility for the same number of data points.

Section 1: Core Mechanics

Michael Parkinson published this estimator in 1980 in a paper titled The Extreme Value Method for Estimating the Variance of the Rate of Return. The core observation: the range between a bar's high and low contains more information about the magnitude of price movement than simply comparing yesterday's close to today's close.

Formula

For each bar, compute the squared log of the high-low ratio. Then average over N bars and annualize:

Where:

• = lookback period (default 20)
• = log of the high-to-low ratio for bar
• = the normalization constant derived from the statistical properties of a Brownian motion process
• = annualization factor for trading days

The constant comes from the mathematical proof that the expected value of for a Brownian motion process equals .

Why It Is More Efficient

Consider a stock that opens at 100, rises to 110, falls back to 100, and closes at 100. The close-to-close return is 0% — Historical Volatility records no movement. But the high-low range of 10% clearly shows significant intraday activity. Parkinson captures this 10% range; standard HV records zero.

Theoretical efficiency advantage: Parkinson's estimator has approximately 1/4 to 1/5 the estimation variance of the close-based estimator. This means 5 days of Parkinson data provides equivalent statistical information to 25 days of close-to-close data.

Inputs

• High: Bar high price
• Low: Bar low price (High and Low only — close not required)
• Period (N): Lookback window for averaging (default 20)

Parameters

Output

Annualized volatility percentage plotted as a single line on a sub-panel. Directly comparable to HV and IV values for the same time period.

Visual Behavior

• Parkinson line runs smoother than HV line — it has lower sampling noise
• During gap events, Parkinson understates volatility (misses the gap; only captures intraday range)
• During high-activity sessions (large intraday swings), Parkinson reads higher than HV

Section 2: Interpretation & Signals

Parkinson vs. HV — When They Diverge

Volatility Regime with Parkinson

Use PV the same way you use HV — as a regime indicator:

• PV at 3-month low → compression; breakout or trend expansion likely
• PV rising rapidly → market becoming increasingly active; widen stops
• PV well above its 90-day average → consider premium selling strategies (IV likely elevated too)

Section 3: Pass vs. Live — Real-Time Reliability

On a live (unclosed) candle, the current bar's high and low are updating continuously. The N-bar Parkinson calculation uses only the prior N closed bars — so the running calculation is stable during the session. The output updates at bar close.

Section 4: Practical Use Cases

Real example: EUR/USD (forex, no daily gaps) in Q2 2023: Parkinson Volatility(20) on the daily chart fell to 4.8% annualized — a 3-year low. HV(20) was 5.1% (close to PV because there are no meaningful gaps in forex). The convergence of both volatility measures at multi-year lows preceded the 4.5% EUR/USD move in June–July 2023 that broke out of the 14-month range. The Parkinson signal was cleaner and had less noise than HV in this case.

Section 5: Pseudo Code

INPUT: high[], low[], period=20, annual_factor=252

PROCESS:
  Step 1: Validate inputs — high[i] must always be >= low[i]
            If high[i] < low[i]: flag data error, return NaN for that bar

  Step 2: Calculate squared log ratio for each bar
            log_hl[i] = ln(high[i] / low[i])
            sq_log_hl[i] = log_hl[i] ^ 2

  Step 3: For each bar i starting from index (period - 1):
            window_sum = sum(sq_log_hl[i-period+1 : i+1])
            parkinson_variance = window_sum / (4 * period * ln(2))
            pv[i] = sqrt(parkinson_variance) * sqrt(annual_factor) * 100

OUTPUT: pv[] — annualized Parkinson Volatility as percentage
EDGE CASES:
  - high[i] == low[i] (doji or halt): ln(1) = 0 — contributes zero to variance (valid, not an error)
  - high[i] / low[i] negative: impossible if prices are positive — flag if it occurs
  - Fewer than period bars: return all NaN
  - Annual factor mismatch: document clearly which factor was used in output metadata

Section 6: Parameters & Optimization

Period Selection Guide

The 5× efficiency advantage means PV(20) is statistically as reliable as HV(100) — a major advantage when you only have limited history.

Section 7: Synergies & Conflicts

Section 8: Common Mistakes

Section 9: Cheat Sheet