ParkinsonVolatility

High-low realised-volatility estimator. Roughly 5× more statistically efficient than close-to-close stddev under driftless Geometric Brownian Motion.

Quick reference

Field	Value
Family	Volatility & Bands
Input type	Candle (uses high, low)
Output type	f64
Output range	[0, ∞) (annualised percent)
Default parameters	period = 20, trading_periods = 252
Warmup period	period (exact)
Interpretation	Annualised realised volatility from bar ranges.

Formula

sigma²  = (1 / (4n · ln 2)) · Σ_{i=1..n} (ln(H_i / L_i))²
sigma   = √sigma²
out     = sigma · √trading_periods · 100

Michael Parkinson (1980) observed that the extreme range of a bar carries more variance information than its closing price alone — a wide bar that closes near its open is far more volatile than a narrow bar that happens to close at the same level. The normalisation constant 1 / (4·ln 2) ≈ 0.3607 (PARKINSON_FACTOR) is evaluated once at const. Under driftless GBM, Parkinson's estimator has roughly 1/5 the variance of the close-to-close estimator.

Parameters

Name	Type	Default	Constraint	Source
period	usize	20	>= 1	ParkinsonVolatility::new (parkinson.rs:70)
trading_periods	usize	252	>= 1	parkinson.rs:70

Either parameter == 0 returns [Error::PeriodZero]. The output is multiplied by 100 so it reads as a percent. Python defaults come from #[pyo3(signature = (period=20, trading_periods=252))]; the Node constructor takes both arguments explicitly.

Inputs / Outputs

use wickra::{Indicator, ParkinsonVolatility, Candle};
// ParkinsonVolatility: Input = Candle, Output = f64
const _: fn(&mut ParkinsonVolatility, Candle) -> Option<f64> = <ParkinsonVolatility as Indicator>::update;

Only high and low are read, so both bindings take just those two series.

• Python. update(candle) returns float | None; batch(high, low) returns a 1-D float64 np.ndarray with NaN warmup.
• Node. update(high, low) returns number | null; batch(high, low) returns an Array<number> with NaN warmup.

Warmup

warmup_period() returns period. The first period − 1 bars only fill the rolling window; the period-th bar produces the first value. Pinned by first_emission_at_warmup_period (period 5: bars 1–4 return None, bar 5 emits).

Edge cases

• Zero-range bars (H == L). ln(H/L) = 0, so the sample is 0; a window of zero-range bars yields 0 (test zero_range_yields_zero).
• Constant-range bars. Identical H/L ratios give a constant output √(factor · (ln H/L)²) · √trading_periods · 100 (test constant_range_yields_constant_sigma).
• Annualisation. trading_periods = 1 returns the raw per-bar σ · 100; otherwise the output scales by √trading_periods.
• Reset. reset() clears the window, running sum-of-squares and last value.

Examples

Rust

use wickra::{BatchExt, Candle, Indicator, ParkinsonVolatility};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let candles: Vec<Candle> = (0..40)
        .map(|i| {
            let base = 100.0 + f64::from(i);
            Candle::new(base, base + 2.0, base - 2.0, base + 1.0, 1.0, i64::from(i)).unwrap()
        })
        .collect();
    let mut pv = ParkinsonVolatility::new(20, 252)?;
    println!("{:?}", pv.batch(&candles).into_iter().flatten().last());
    Ok(())
}

Python

import numpy as np
import wickra as ta

pv = ta.ParkinsonVolatility(20, 252)
out = pv.batch(high, low)  # 1-D annualised-% series, NaN warmup

Node

const ta = require('wickra');
const pv = new ta.ParkinsonVolatility(20, 252);
const v = pv.update(102, 98); // null during warmup, else annualised %

Interpretation

Parkinson is the simplest of the range-based volatility estimators — it uses only the high-low spread:

1. Level reading. Annualised percent, comparable across regimes.
2. Use and limits. Cheaper (high/low only) and more efficient than close-to-close, but it ignores both the open-to-close body and overnight gaps, so it under-estimates volatility on trending or gappy data. GarmanKlassVolatility adds the body; YangZhangVolatility adds gaps.

Common pitfalls

• Using it where the open-to-close move matters. Two bars with the same range but very different bodies get the same Parkinson reading — by construction.
• Treating it as gap-aware. It only sees within-bar range; overnight jumps are invisible to it.

References

• Michael Parkinson, The Extreme Value Method for Estimating the Variance of the Rate of Return, The Journal of Business, vol. 53, no. 1, 1980, pp. 61–65.

See also

• HistoricalVolatility — close-to-close baseline.
• GarmanKlassVolatility — adds an open-to-close term; ~7.4× efficient.
• RogersSatchellVolatility — drift-free OHLC estimator.
• YangZhangVolatility — gold standard combining all three.