GarmanKlass

Garman-Klass refers to a volatility estimator introduced by Mark W. Garman and Klass in 1980 that uses daily high, low, open, and close prices to estimate the volatility of an asset. It is designed to improve efficiency over the standard close-to-close estimator by incorporating intraday price information, specifically the range between intraday highs and lows.

The daily variance estimate is commonly given by the formula: sigma^2_GK = 0.5 [ln(H/L)]^2 - (2 ln 2 - 1) [ln(C/O)]^2, where H is the intraday high, L is the intraday low, O is the opening price, C is the closing price, and ln denotes the natural logarithm. This yields an estimate of the variance of log returns over the day; volatility can be obtained by taking the square root. For longer horizons, daily estimates can be aggregated, and annualization is typically performed by scaling with the appropriate factor (for example, multiplying by the square root of the number of trading days).

The GK estimator rests on a continuous-time log-price model with limited drift over a trading day and is one of several intraday-based volatility estimators intended to exploit more information than close-to-close methods. It is often discussed alongside related estimators such as Parkinson’s (which uses only high-low) and Rogers-Satchell (which addresses drift more explicitly). Limitations include sensitivity to microstructure noise, opening or closing jumps, and violations of its underlying assumptions.

Applications of the Garman-Klass estimator appear in financial research, risk management, and model calibration where accurate realization of volatility from daily data is beneficial.