# Parkinson volatility estimator

Parkinson volatility estimator is a measure of historical price variability that uses a stock’s daily highs and lows, rather than its closing prices, to estimate volatility.

## What it means

A stock can move substantially during a session yet finish near its previous close. A measure based only on closing prices may miss that intraday movement. The Parkinson volatility estimator instead uses each trading day’s highest and lowest prices to estimate historical volatility.

Its result describes variability over an observed period, not the direction of the next move. A *daily* estimate is expressed as a proportion of price per trading day; multiplying it by 100 expresses it as a daily percentage. It is not a percentage change or a forecast of tomorrow’s range.

## How it is calculated

For `n` trading days, the conventional daily Parkinson estimate is:

`σ_P,daily = sqrt([Σ from i=1 to n of (ln(H_i/L_i))²] / [4n ln(2)])`

- `σ_P,daily` is estimated daily volatility, expressed as a decimal.
- `H_i` is the stock’s highest price on trading day `i`, in the same currency and price units as `L_i`.
- `L_i` is its lowest price on that day; it must be greater than zero.
- `ln` is the natural logarithm, and `Σ` means add the values across all observed days.
- `n` is the number of trading days. The constant `4 ln(2)` comes from the assumptions underlying the estimator.

The ratio `H_i/L_i` has no units, so the result does not depend on whether prices are quoted in dollars or cents. To annualize a daily estimate using an assumed `D` trading days per year, use `σ_P,annual = σ_P,daily × sqrt(D)`. State the chosen `D` when comparing annualized figures.

## Worked example

Suppose a hypothetical stock records the same high of US$110 and low of US$100 on each of four trading days. These round prices make the arithmetic easier to follow; they are not market data.

1. For each day, divide high by low: `110 / 100 = 1.10`.
2. Take the natural logarithm and square it: `ln(1.10) ≈ 0.09531`; `(0.09531)² ≈ 0.009084`.
3. Add the four squared values: `4 × 0.009084 ≈ 0.036336`.
4. Divide by `4 × 4 × ln(2) ≈ 11.09035`, then take the square root: `sqrt(0.036336 / 11.09035) ≈ 0.05724`.

The estimated **daily volatility is about 5.72%**. It is not the same as the day’s 10% high-to-low ratio: the estimator applies a logarithm, averaging and a scaling constant. Nor does 5.72% mean the stock will move exactly that much on the next trading day.

## Why it matters before you trade

Pre-trade analysis considers how much a stock has moved, alongside liquidity and the proposed order. High-low data can reveal intraday variation that a close-to-close calculation overlooks. A volatility estimate can therefore inform a risk check or an assessment of execution conditions.

The distinction matters around overnight events. A stock might close at US$100, open the next day at US$90 and trade only between US$89 and US$91. Its narrow range that day does not capture the full close-to-open gap. A high-low estimate alone can understate risk when overnight moves matter. It also says nothing by itself about how many shares are available or what an order will cost to execute.

## How PreTrAIde uses it

PreTrAIde includes the Parkinson estimator among the methods blended in its deterministic daily-volatility calculation. The other stated components are close-to-close, Yang-Zhang and simplified GARCH(1,1) estimators. Its pre-trade analysis also includes a 1-day 95% value at risk and 0–100 volatility scores for each stock and the basket.

Those measures contribute to decision support before an order is placed; a volatility estimate alone is not a PreTrAIde verdict. PreTrAIde’s GO, NO-GO and MODIFY verdicts are not investment recommendations, and users place any trades themselves with their own broker.

## Common mistakes

- **Treating a range as a prediction.** Historical volatility measures past variability; it does not specify the next day’s return or direction.
- **Ignoring gaps.** Daily highs and lows exclude the price move between the previous close and the next open.
- **Mixing time scales.** A daily estimate and an annualized estimate are not directly comparable without conversion.
- **Using unadjusted or mismatched data.** Stock splits or inconsistent high-low observations can distort the calculation; prices should be checked for comparability.
- **Equating volatility with execution cost.** Spread, liquidity and market impact require separate assessment.

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Source: https://pretraide.com/glossary/parkinson-volatility