Parkinson Volatility Estimator

The Parkinson volatility estimator is a method of estimating the volatility of an asset from the highest and lowest prices traded in each period, instead of from closing prices alone. Because the high and the low record the extremes of the whole day's trading, they carry more information about how much the price moved than a single closing value does. The estimator was introduced by the physicist Michael Parkinson in a paper published in 1980.

It belongs to the family of range-based volatility estimators, which are used by quantitative analysts and risk managers to measure realized volatility more precisely from daily data. It requires only the high price and the low price of each day, which are available for almost every traded instrument.

The estimate of variance over $n$ periods is:

• $\sigma_P^{2}$ is the estimated variance per period, and its square root is the volatility.
• $H_i$ is the highest traded price in period $i$.
• $L_i$ is the lowest traded price in period $i$.
• $n$ is the number of periods, usually days.
• $\ln$ is the natural logarithm, and $4 \ln 2$ is approximately 2.773.

The constant comes from the mathematics of Brownian motion. If the logarithm of the price follows a driftless random process with constant volatility, the expected squared range over a period equals $4 \ln 2$ times the variance. Dividing the average squared range by that constant therefore recovers the variance.

Suppose a share's high for the day is 102 and its low is 99. The log range is $\ln(102 / 99) = 0.02985$, and its square is 0.000891. Dividing by 2.773 gives a daily variance of 0.000321, and the square root gives a daily volatility of 0.01793, or 1.79 percent. To annualise, the daily figure is multiplied by the square root of the number of trading days in a year: $0.01793 \times \sqrt{252} = 0.285$, or about 28.5 percent. In practice the calculation is averaged over many days, such as 20 or 60, to reduce noise.

The standard method computes the standard deviation of daily returns from one closing price to the next. It uses two prices a day and ignores everything in between. A day on which the price swings widely but closes unchanged contributes nothing to the close-to-close figure and a great deal to the range. Under the assumptions of the model, Parkinson's estimator is about five times as efficient as the close-to-close estimator, meaning that it reaches the same statistical precision with roughly a fifth as many days of data. This matters when volatility is changing, since an estimate from a short, recent window is more relevant than one from a long window.

• Overnight moves. The estimator sees only what happens while the market is open. Price jumps between one day's close and the next day's open are missed, so for shares, which often gap at the open, it understates total volatility.
• Drift. The derivation assumes no trend. In a strongly trending market, part of the day's range reflects the trend, and the estimate is biased upward.
• Discrete trading. The theory assumes the price is observed continuously. In reality trades occur at intervals, so the recorded high is at or below the true maximum and the recorded low at or above the true minimum. The observed range is too small, and the estimate is biased downward, most severely for thinly traded instruments.
• Data quality. A single erroneous trade can set a day's high or low. Because the range is squared, bad ticks distort the result, and the highs and lows reported by different data vendors may not agree.
• Jumps and changing volatility. The assumption of constant volatility within the day does not hold around news releases or at the open and close.

Later estimators extend the idea by adding more price points. The Garman-Klass estimator, also from 1980, combines the range with the opening price and the close and is more efficient still. The Rogers-Satchell estimator allows for drift. The Yang-Zhang estimator adds the overnight move and is designed to handle both drift and opening gaps. All can be computed from the four prices drawn on a candlestick chart.

Where intraday data are available, analysts often measure volatility directly by summing squared returns over short intervals, which uses far more information than any daily estimator. Range-based methods remain useful where only daily data exist, for long histories, and as a check that is less sensitive to the noise in very high-frequency prices.

Range-based estimates feed several tasks. They serve as inputs to volatility forecasting, sometimes inside models of the GARCH type that use the range in place of squared returns. Option traders compare them with implied volatility to judge whether options are cheap or expensive. Portfolio managers use them to scale positions in volatility targeting, where a more responsive estimate allows faster adjustment. A persistent gap between the Parkinson figure and the close-to-close figure is itself informative: a much higher range-based number indicates large swings within the day that reverse before the close.