Quantitative Finance

Yang-Zhang Minimum-Variance OHLC Volatility Formula (Overnight + Intraday)

Combine overnight gap variance v_o, open-to-close variance v_c, and Rogers-Satchell intraday variance v_rs using Yang & Zhang’s (2000) optimal weight k = 0.34 / (1.34 + (N + 1)/(N - 1)).

Capture both overnight earnings gaps and intraday wicks without drift bias!

Pure intraday OHLC estimators (including Garman-Klass and Rogers-Satchell) are blind to overnight opening jumps between yesterday’s Close C_{t-1} and today’s Open O_t! Yang & Zhang (2000) derived the minimum-variance unbiased estimator independent of both continuous drift AND opening jumps by combining Overnight Variance v_o = VAR.S(LN(O_t / C_{t-1})), Open-to-Close Variance v_c = VAR.S(LN(C_t / O_t)), and Mean Rogers-Satchell Variance v_rs!

For sample window length N >= 2 days, the variance-minimizing weight on open-to-close variance is k = 0.34 / (1.34 + (N + 1) / (N - 1)), giving Total Daily Variance v_YZ = v_o + k * v_c + (1 - k) * v_rs and Annualized Volatility = SQRT(252 * v_YZ).

Variance Component (N = 21 Days)	Daily Variance	Weight in Yang-Zhang	Contribution
Overnight Jump Variance (v_o)	0.000120	1.0000	0.0001200
Open-to-Close Variance (v_c)	0.000250	k = 0.1393	0.0000348
Rogers-Satchell Intraday (v_rs)	0.000180	1 - k = 0.8607	0.0001549 (Ann Vol = 27.9389%)

Annualized Yang-Zhang Volatility % from Component Variances

Computes optimal weight k from N = B5, blends v_o (B2), v_c (B3), and v_rs (B4), and annualizes over B6 trading days.

=IF(OR(B2 < 0, B3 < 0, B4 < 0, B5 < 2, B6 <= 0), "Invalid Variance or Sample N", ROUND(100 * SQRT(B6 * (B2 + (0.34 / (1.34 + (B5 + 1) / (B5 - 1))) * B3 + (1 - (0.34 / (1.34 + (B5 + 1) / (B5 - 1)))) * B4)), 4))

Optimal Open-to-Close Weight k(N) & Overnight Jump Variance Share %

Calculates Yang-Zhang weight k = 0.34 / (1.34 + (N + 1) / (N - 1)).

=IF(B5 < 2, 0, ROUND(0.34 / (1.34 + (B5 + 1) / (B5 - 1)), 4))

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