wickra/docs/wiki/indicators/volatility-bands/Indicator-HistoricalVolatility.md

HistoricalVolatility

Historical Volatility — the annualised standard deviation of log returns, the realised volatility used to price options and size risk.

Quick reference

Field	Value
Family	Volatility & Bands
Input type	f64 (single close)
Output type	f64
Output range	[0, ∞) (annualised percent)
Default parameters	(period = 20, trading_periods = 252) (Python)
Warmup period	period + 1
Interpretation	Annualised volatility of returns, in percent.

Formula

r_t = ln(price_t / price_{t−1})
HV  = stddev_sample(r over period) · √trading_periods · 100

The log returns over the window are measured with the sample standard deviation (divisor n − 1, Bessel's correction — the unbiased volatility estimator), then annualised by √trading_periods and expressed as a percentage. trading_periods is the number of bars in a year for the data's frequency: 252 for daily bars, 52 for weekly, 12 for monthly.

Parameters

Name	Type	Default	Valid range	Description
period	usize	20 (Python)	>= 2	Number of log returns in the window. 0 errors with Error::PeriodZero; 1 with Error::InvalidPeriod (the sample stddev needs two returns).
trading_periods	usize	252 (Python)	>= 1	Annualisation factor. 0 errors with Error::PeriodZero.

The Python binding defaults the pair to (20, 252). The periods property returns (period, trading_periods).

Inputs / Outputs

From crates/wickra-core/src/indicators/historical_volatility.rs:

impl Indicator for HistoricalVolatility {
    type Input = f64;
    type Output = f64;
    // update(&mut self, input: f64) -> Option<f64>
}

A single f64 close in, an Option<f64> out. Python maps this to float | None / numpy.ndarray (NaN warmup); Node to number | null / Array<number> (NaN warmup).

Warmup

warmup_period() == period + 1. The first log return needs a previous price, and the window must then hold period returns — so the first non-None output lands on input period + 1.

Edge cases

• Constant series. A flat price series has all log returns equal to 0, so volatility is 0.0 (constant_series_yields_zero pins this).
• Geometric series. A constant growth factor produces a constant log return; its standard deviation — and so HV — is 0 (geometric_series_yields_zero pins this).
• Non-positive prices. A log return is undefined when either price is <= 0; that return is treated as 0.
• Non-negative. Volatility is a standard deviation and is never negative (output_is_non_negative pins this).
• NaN / infinity inputs. Non-finite inputs are silently dropped.
• Reset. hv.reset() clears the previous price, the window and the running sums.

Examples

Rust

use wickra::{BatchExt, Indicator, HistoricalVolatility};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // 20-bar window, 252 trading days per year.
    let mut hv = HistoricalVolatility::new(20, 252)?;
    let prices: Vec<f64> = (0..40).map(|i| 100.0 * 1.01_f64.powi(i)).collect();
    let out = hv.batch(&prices);
    println!("warmup_period = {}", hv.warmup_period());
    // A perfectly geometric series has constant returns -> zero volatility.
    println!("last = {:?}", out.last().unwrap());
    Ok(())
}

Output:

warmup_period = 21
last = Some(0.0)

Python

import numpy as np
import wickra as ta

hv = ta.HistoricalVolatility()  # (period=20, trading_periods=252)
prices = np.full(40, 100.0)  # flat series
print(hv.batch(prices)[-1])  # no return variation -> 0

Output:

0.0

Node

const ta = require('wickra');
// 52 trading periods per year for weekly bars.
const hv = new ta.HistoricalVolatility(20, 52);
const prices = Array.from({ length: 60 }, (_, i) => 100 + Math.sin(i * 0.3) * 5);
console.log('warmupPeriod:', hv.warmupPeriod());

Interpretation

HistoricalVolatility is the realised-volatility number quoted in options and risk work — "this stock has been running at 30 % annualised vol". Compare it against an option's implied volatility to judge whether options are cheap or rich, feed it into position-sizing (smaller size as HV rises), or track its own trend: volatility clusters, so a rising HV tends to keep rising.

Always match trading_periods to your bar frequency — annualising daily bars with 252, weekly with 52, monthly with 12. Using the wrong factor rescales every reading.

Common pitfalls

• Mismatched trading_periods. Annualising weekly data with 252 inflates HV by √(252/52) ≈ 2.2×.
• Confusing it with StdDev. StdDev is the population dispersion of prices; HistoricalVolatility is the sample (n − 1) dispersion of log returns, annualised.

References

Historical (realised) volatility is the standard √252-annualised standard deviation of log returns; the unbiased n − 1 estimator is the conventional choice for volatility estimation.

See also

• Indicator-StdDev.md — population dispersion of raw prices.
• Indicator-Natr.md — range-based volatility as a percentage.
• Indicators-Overview.md — the full taxonomy.