RogersSatchellVolatility

Drift-free OHLC realised-volatility estimator. Exact under arbitrary Brownian drift — the drift component cancels algebraically.

Quick reference

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

Formula

s_t   = ln(H_t / C_t) · ln(H_t / O_t) + ln(L_t / C_t) · ln(L_t / O_t)
sigma = √max(mean(s_t over `period`), 0)
out   = sigma · √trading_periods · 100

Rogers, Satchell & Yoon (1994) extended the Garman-Klass framework to handle non-zero drift without introducing bias. The per-bar sample is guaranteed non-negative by construction: Candle::new enforces H >= max(O, L, C) and L <= min(O, H, C), which makes ln(H/·) >= 0 and ln(L/·) <= 0, so both products contribute non-negative terms.

Parameters

Name	Type	Default	Constraint	Source
period	usize	20	>= 1	RogersSatchellVolatility::new (rogers_satchell.rs:68)
trading_periods	usize	252	>= 1	rogers_satchell.rs:68

Either parameter == 0 returns [Error::PeriodZero]. trading_periods is the annualisation factor (252 daily, 52 weekly, 12 monthly, 1 for raw per-bar volatility). Python defaults come from #[pyo3(signature = (period=20, trading_periods=252))]; the Node constructor takes both arguments explicitly.

Inputs / Outputs

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

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

Warmup

warmup_period() returns period. The rolling mean of the per-bar samples needs a full period window, so the first non-None output lands on bar period (index period − 1). Pinned by first_emission_at_warmup_period (period 5: bars 1–4 return None, bar 5 emits).

Edge cases

• Zero-movement bars (O == H == L == C). Every log term is zero; the estimator returns 0 (test zero_movement_yields_zero).
• Constant bar shape. Identical OHLC ratios every bar give a constant output √k · √trading_periods · 100 (test constant_bar_shape_yields_constant_sigma).
• Strong intraday trend. Unlike Garman-Klass, the estimator stays unbiased — this is its defining advantage.
• Overnight gaps. Rogers-Satchell ignores close-to-open variance. For data with material gaps, use YangZhangVolatility.
• Reset. reset() clears the window, running sum and last value.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let candles: Vec<Candle> = (0..40)
        .map(|i| {
            let base = 100.0 + f64::from(i);
            // open, high, low, close, volume, ts
            Candle::new(base, base + 2.0, base - 2.0, base + 0.5, 1.0, i64::from(i)).unwrap()
        })
        .collect();
    let mut rs = RogersSatchellVolatility::new(20, 252)?;
    println!("{:?}", rs.batch(&candles).into_iter().flatten().last()); // annualised %
    Ok(())
}

Python

import numpy as np
import wickra as ta

rs = ta.RogersSatchellVolatility(20, 252)
out = rs.batch(open_, high, low, close)  # 1-D annualised-% series, NaN warmup

Node

const ta = require('wickra');
const rs = new ta.RogersSatchellVolatility(20, 252);
const v = rs.update(100, 102, 98, 100.5); // null during warmup, else annualised %

Interpretation

Rogers-Satchell answers "how volatile is this asset?" using the full bar geometry, and crucially does so without being fooled by a steady trend:

1. Level reading. The output is an annualised volatility percentage — 30.0 means ≈ 30 % annualised. Compare it across regimes to gauge expansion/contraction.
2. Drift immunity. A strongly trending instrument inflates close-to-close and Garman-Klass estimates; Rogers-Satchell removes that bias, so it is the right choice for trending assets without overnight gaps.

Common pitfalls

• Using it on gappy data. It ignores the close-to-open jump, so on equities/futures with overnight gaps it under-estimates true volatility — switch to YangZhangVolatility.
• Forgetting the annualisation factor. With trading_periods = 252 the output is annualised; pass 1 if you want the raw per-bar figure.

References

• L. C. G. Rogers, S. E. Satchell & Y. Yoon, Estimating the Volatility of Stock Prices: A Comparison of Methods that Use High and Low Prices, Applied Financial Economics, vol. 4, 1994, pp. 241–247.

See also

• GarmanKlassVolatility — slightly more efficient but biased under drift.
• YangZhangVolatility — adds overnight variance.
• ParkinsonVolatility — high-low only.
• HistoricalVolatility — close-to-close baseline.