Yang-Zhang volatility estimator

What it means

A stock can move while its exchange is closed and continue moving during the next trading session. The Yang-Zang estimator uses daily opening, high, low, and closing prices, plus the previous close, to capture both parts of that movement. It estimates historical volatility: the variability observed over a chosen sample, not the direction or size of the next move.

Its components separate overnight gaps, intraday open-to-close returns, and intraday high-low ranges. The result is expressed as a standard deviation of log returns per trading day when calculated from daily prices. Like other historical estimators, it depends on the observation window and the quality of the price data.

How it is calculated

For n trading days, with n > 2, one common form is:

σ_YZ² = σ_O² + kσ_C² + (1 − k)σ_RS²; k = 0.34 / [1.34 + (n + 1)/(n − 1)]

• O_i, H_i, L_i, and C_i are day i’s open, high, low, and close prices, all in the same currency; C_(i−1) is the preceding trading day’s close.
• o_i = ln(O_i / C_(i−1)) is the overnight log return. σ_O² is the sample variance of the n values of o_i.
• c_i = ln(C_i / O_i) is the intraday log return. σ_C² is the sample variance of the n values of c_i.
• RS_i = ln(H_i / C_i) ln(H_i / O_i) + ln(L_i / C_i) ln(L_i / O_i) is the Rogers-Satchell high-low variance term. σ_RS² is the average of the n values of RS_i, not their sample variance.
• k is a dimensionless weighting factor. σ_YZ² is daily log-return variance; σ_YZ = √σ_YZ² is daily volatility. Multiply σ_YZ by 100 to express it as a percentage.

All component returns are dimensionless. The sample variances use n − 1 in their denominators, while the Rogers-Satchell average uses n.

Worked example

The following component values are hypothetical, supplied to illustrate the final calculation rather than derived from a price series. Suppose a 21-trading-day sample gives overnight sample variance σ_O² = 0.000100, intraday sample variance σ_C² = 0.000225, and average Rogers-Satchell term σ_RS² = 0.000196.

1. Calculate the weight: k = 0.34 / [1.34 + 22/20] ≈ 0.13934.
2. Combine the components: σ_YZ² = 0.000100 + 0.13934 × 0.000225 + 0.86066 × 0.000196 ≈ 0.000300.
3. Take the square root: σ_YZ ≈ √0.000300 ≈ 0.0173, or 1.73% daily volatility.

This is a variability estimate, not a statement that tomorrow’s return will be 1.73%.

Why it matters before you trade

An overnight gap may be missed by a measure based only on close-to-close movements within a session or only on intraday ranges. Including both overnight and intraday information can make a pre-trade risk check more informative when a stock has meaningful opening gaps.

Volatility helps put a proposed position’s short-horizon price risk in context, but it is not the same as liquidity or execution cost. A volatility estimate also cannot specify a worst-case loss: unusual events can exceed what a historical sample suggests.

How PreTrAIde uses it

PreTrAIde’s quantitative layer blends Yang-Zhang with Parkinson, close-to-close, and simplified GARCH(1,1) estimators to calculate daily volatility. That layer also calculates a 1-day 95% value at risk and 0–100 volatility scores for each stock and the basket. Pre-trade analysis returns a risk assessment and plain-language reasoning alongside its GO, NO-GO, or MODIFY verdict. Those verdicts are decision support, not trade recommendations.

Common mistakes

• Treating it as a forecast: It summarizes historical movements; future volatility can differ.
• Dropping the previous close: The overnight return requires C_(i−1), so n measured days need an earlier closing price.
• Mixing methods or units: The Rogers-Satchell term is averaged, not sample-varianced; variance must be square-rooted before reporting volatility as a percentage.
• Ignoring price adjustments: Splits or inconsistent price series can introduce artificial returns and distort the estimate.