RealizedVolatility

The square root of the sum of squared log returns over a window — raw, un-annualised quadratic variation, the high-frequency volatility estimator.

Quick reference

Field	Value
Family	Price Statistics
Input type	f64 (single price)
Output type	f64
Output range	>= 0
Default parameters	period is required
Warmup period	period + 1
Interpretation	Higher = more realised variation over the window. Multiply by √trading_periods to annualise.

Formula

r_t = ln(price_t / price_{t−1})
RV  = √( Σ r_t²  over the last `period` returns )

Unlike HistoricalVolatility — which reports the annualised sample standard deviation of log returns (mean-centred, divided by n − 1, scaled by √trading_periods, ×100) — realized volatility is the raw, un-centred, un-annualised quadratic-variation estimator from high-frequency econometrics. It makes no Gaussian assumption and no mean subtraction: it simply accumulates squared returns, converging to the integrated variance of the price path as the sampling frequency rises.

Source: crates/wickra-core/src/indicators/realized_volatility.rs.

Parameters

Name	Type	Default	Valid range	Source	Description
period	usize	none	>= 1	realized_volatility.rs:62	Number of squared log returns summed. period = 0 errors with Error::PeriodZero.

Inputs / Outputs

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

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

Python streams as float | None, batches as a 1-D numpy.ndarray. Node streams as number | null, batches as Array<number>.

Warmup

warmup_period() == period + 1: one price seeds the previous-price reference, then period returns fill the window. The unit test accessors_and_metadata pins warmup_period() == 21 for period = 20; first_emission_at_warmup_period pins the first Some at index period.

Edge cases

• Constant series. Flat prices give zero returns, so RV = 0. The unit test constant_series_yields_zero pins this.
• Non-negativity. RV is a square root of a non-negative sum; the unit test output_is_non_negative pins v >= 0 over a noisy path.
• Non-finite / non-positive prices. Skipped (the log return is undefined); state is untouched and the last value returned. Pinned by ignores_non_finite_input and skips_non_positive_prices.
• Reset. reset() clears the window and the previous-price reference.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut rv = RealizedVolatility::new(2)?;
    let out: Vec<Option<f64>> = rv.batch(&[100.0, 110.0, 121.0]);
    println!("{:?}", out);
    Ok(())
}

Output:

[None, None, Some(0.13478635600636957)]

Two equal +10% steps give r = ln(1.1) each, so RV = √(2 · ln(1.1)²) ≈ 0.1348. This matches the known_value unit test.

Python

import wickra as ta

rv = ta.RealizedVolatility(2)
for x in [100.0, 110.0, 121.0]:
    print(x, '->', rv.update(x))

Output:

100.0 -> None
110.0 -> None
121.0 -> 0.13478635600636957

Node

const ta = require('wickra');
const rv = new ta.RealizedVolatility(2);
for (const x of [100, 110, 121]) console.log(x, '->', rv.update(x));

Output:

100 -> null
110 -> null
121 -> 0.13478635600636957

Interpretation

RealizedVolatility is the model-free volatility measure for intrabar / tick data: feed high-frequency prices and read off the realised variation of the path. Because it is un-annualised, compare readings only at the same sampling frequency, or multiply by √trading_periods for an annual figure. When you want the classical annualised, mean-centred, percentage volatility for options / risk, use HistoricalVolatility instead.

Common pitfalls

• Treating it as annualised. The output is raw √Σr²; it scales with √period. Two RealizedVolatility instances of different periods are not directly comparable without normalising.
• Comparing to HistoricalVolatility. The two use different definitions (un-centred sum vs mean-centred sample variance, un-annualised vs ×√252×100). They will not match numerically; pick the one matching your convention.

References

Andersen, Bollerslev, Diebold & Labys, "The Distribution of Realized Exchange Rate Volatility" (2001); Barndorff-Nielsen & Shephard on realised variance and quadratic variation.

See also

• Indicator-HistoricalVolatility — annualised sample-stddev volatility.
• Indicator-LogReturn — the returns summed here.
• Indicators-Overview — the full taxonomy.