"Yang-Zhang vs Close-to-Close: Which Realized Volatility Estimator Should You Use?"

The Problem: Measuring "How Volatile" a Stock Has Been

Every options trader needs a number for realized volatility (RV). You need it to compute the volatility risk premium — the spread between implied and realized vol that drives premium-selling strategies. You need it to calibrate models, backtest systems, and assess whether options are cheap or expensive.

But realized volatility is not a single number. It depends entirely on how you measure it. The simplest estimator — close-to-close — throws away most of the information in your price data. More sophisticated estimators use open, high, low, and close (OHLC) prices to extract more signal from the same data. The question is: which one should you use?

Close-to-Close: The Baseline

The close-to-close estimator is the simplest and most widely used. It computes volatility as the standard deviation of log returns, annualized:

Where C_t is the closing price on day t, n is the number of observations, and r̄ is the mean log return. The factor of 252 annualizes from daily to yearly.

The core limitation is efficiency. In statistics, efficiency measures how much information an estimator extracts from available data. Close-to-close uses exactly one data point per day (the close), discarding everything that happened between open and close. A stock that gaps up 3%, drops 5%, and recovers to close unchanged had a volatile day — but CC says nothing happened.

Parkinson: Using the High-Low Range

Parkinson (1980) recognized that the daily high-low range contains far more information about volatility than closing prices alone. His estimator:

Where H_t and L_t are the high and low prices on day t. The constant 1/(4 ln 2) comes from the theoretical relationship between range and volatility under geometric Brownian motion.

Parkinson is approximately 5 times more efficient than close-to-close, meaning it achieves the same estimation accuracy with one-fifth as many observations. A 10-day Parkinson estimate is roughly as accurate as a 50-day close-to-close estimate.

Garman-Klass: Adding Open and Close

Garman and Klass (1980) extended Parkinson by incorporating open and close prices alongside the high-low range. Their estimator partially corrects for the overnight gap bias:

Where O_t is the opening price. The first term captures the range-based information (similar to Parkinson), and the second term adjusts for the open-to-close return, which partially accounts for overnight gaps by anchoring the estimate to the open.

Garman-Klass is roughly 7-8 times more efficient than close-to-close. However, it still assumes that the opening price equals the previous close — a violation in any market with overnight sessions, pre-market trading, or earnings announcements.

Yang-Zhang: The Complete Estimator

Yang and Zhang (2000) developed an estimator that explicitly handles overnight gaps, intraday drift, and open-to-close variance. It combines three components:

Where:

• σ_o² = variance of overnight returns (close-to-open): ln(O_t/C_t-1)
• σ_c² = variance of open-to-close returns: ln(C_t/O_t)
• σ_RS² = Rogers-Satchell variance (a range-based estimator that handles drift)
• k = weighting constant, typically k = 0.34 / (1.34 + (n+1)/(n-1))

The Rogers-Satchell component itself is:

This three-component architecture is what makes Yang-Zhang unique. The overnight variance captures gap risk. The open-to-close variance captures intraday drift. The Rogers-Satchell component captures range-based volatility without drift bias. The weighted combination produces the minimum-variance unbiased estimator for daily OHLC data.

Efficiency Comparison

Efficiency measures how much variance reduction an estimator achieves relative to close-to-close. Higher efficiency means the estimator converges to the true volatility faster with fewer data points.

The practical implication: a 5-day Yang-Zhang estimate carries roughly the same statistical precision as a 70-day close-to-close estimate. For short-window VRP calculations — where you need a responsive RV measure — this difference is enormous.

What FlashAlpha Uses

The FlashAlpha Volatility Analysis endpoint (/v1/volatility/{symbol}) returns realized volatility across five lookback windows: 5-day, 10-day, 20-day, 30-day, and 60-day. These are computed using the Yang-Zhang estimator, giving you a high-efficiency RV estimate that properly accounts for overnight gaps and intraday range.

from flashalpha import FlashAlphaClient

client = FlashAlphaClient(api_key="your_api_key")
vol = client.get_volatility("SPY")

print(f"SPY Realized Volatility (Yang-Zhang):")
print(f"  RV  5d:  {vol['realized_vol']['rv_5d']}%")
print(f"  RV 10d:  {vol['realized_vol']['rv_10d']}%")
print(f"  RV 20d:  {vol['realized_vol']['rv_20d']}%")
print(f"  RV 30d:  {vol['realized_vol']['rv_30d']}%")
print(f"  RV 60d:  {vol['realized_vol']['rv_60d']}%")
print(f"  ATM IV:  {vol['atm_iv']}%")
print(f"  VRP:     {vol['iv_rv_spreads']['vrp_20d']}%")

The VRP spread (vrp_20d) is computed as ATM IV minus 20-day Yang-Zhang RV. Because the RV estimate is high-efficiency, the VRP signal is more stable and responsive than if you used close-to-close — fewer false signals, faster regime detection.

Python: Compute All Four Estimators from OHLC Data

Here is a complete implementation of all four estimators so you can compare them on your own data:

import numpy as np
import pandas as pd
import yfinance as yf

def close_to_close(df, window=20):
    """Standard close-to-close realized volatility."""
    log_returns = np.log(df['Close'] / df['Close'].shift(1))
    return log_returns.rolling(window).std() * np.sqrt(252) * 100

def parkinson(df, window=20):
    """Parkinson (1980) high-low range estimator."""
    log_hl = np.log(df['High'] / df['Low'])
    factor = 252 / (4 * window * np.log(2))
    return np.sqrt(factor * (log_hl ** 2).rolling(window).sum()) * 100

def garman_klass(df, window=20):
    """Garman-Klass (1980) OHLC estimator."""
    log_hl = np.log(df['High'] / df['Low'])
    log_co = np.log(df['Close'] / df['Open'])
    term1 = 0.5 * log_hl ** 2
    term2 = (2 * np.log(2) - 1) * log_co ** 2
    return np.sqrt((252 / window) * (term1 - term2).rolling(window).sum()) * 100

def yang_zhang(df, window=20):
    """Yang-Zhang (2000) estimator with overnight, intraday, and RS components."""
    log_oc = np.log(df['Open'] / df['Close'].shift(1))  # overnight
    log_co = np.log(df['Close'] / df['Open'])            # open-to-close

    # Rogers-Satchell component
    log_hc = np.log(df['High'] / df['Close'])
    log_ho = np.log(df['High'] / df['Open'])
    log_lc = np.log(df['Low'] / df['Close'])
    log_lo = np.log(df['Low'] / df['Open'])
    rs = log_hc * log_ho + log_lc * log_lo

    # Variances (rolling)
    k = 0.34 / (1.34 + (window + 1) / (window - 1))
    overnight_var = log_oc.rolling(window).var()
    close_var = log_co.rolling(window).var()
    rs_var = rs.rolling(window).mean()

    yz_var = overnight_var + k * close_var + (1 - k) * rs_var
    return np.sqrt(yz_var * 252) * 100

# --- Compare estimators on SPY ---
spy = yf.download("SPY", period="1y")

results = pd.DataFrame({
    'Close-to-Close': close_to_close(spy, 20),
    'Parkinson': parkinson(spy, 20),
    'Garman-Klass': garman_klass(spy, 20),
    'Yang-Zhang': yang_zhang(spy, 20)
})

print(results.tail(10).round(2).to_string())
print(f"\nLatest 20-day estimates:")
for col in results.columns:
    print(f"  {col:20s}: {results[col].iloc[-1]:.2f}%")

You will typically observe that Parkinson and Garman-Klass run slightly below close-to-close (because they miss overnight gaps), while Yang-Zhang tracks close to close-to-close on average but with much less noise. The spread between estimators widens during earnings season and macro events — exactly when the overnight gap component matters most.

Practical Guidance: When to Use Which

There is no universally "best" estimator — the right choice depends on your use case, data quality, and the market structure of what you're trading.

Why This Matters for VRP

The volatility risk premium is defined as:

Your choice of RV estimator directly changes the VRP number you compute. Consider a concrete example:

Same stock, same period, three different VRP readings: 3.8% (CC), 7.3% (Parkinson), and 2.6% (YZ). Parkinson says premium is rich. Yang-Zhang says it's modest. The difference is that Parkinson missed overnight gaps that added real volatility, making RV look artificially low and VRP look artificially high. Acting on the Parkinson signal could lead you to sell premium that isn't actually overpriced.

Related Reading

• Realized vs Implied Volatility and the Risk Premium — deep dive into VRP theory and strategy
• IV Rank vs IV Percentile — which metric to use when assessing implied volatility levels
• Volatility Surface API — build and visualize IV surfaces in Python
• Volatility API Documentation — endpoint reference for /v1/volatility/{symbol}

Frequently Asked Questions