// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Yang-Zhang Volatility (YZV)", shorttitle="YZV", overlay=false)

//@function Calculates Yang-Zhang Volatility (YZV)
//@param length Lookback period for smoothing daily variance estimates (> 0)
//@returns Yang-Zhang Volatility value for the current bar
//@optimized Uses bias-corrected RMA with OHLC prices for O(1) complexity per bar
yzv(int length) =>
    o=open,h=high,l=low,c=close,pc=na(close[1])?open:close[1]
    ro=math.log(o/pc),rc=math.log(c/o),rh=math.log(h/o),rl=math.log(l/o)
    s_o_sq=ro*ro,s_c_sq=rc*rc
    s_rs_sq=rh*(rh-rc)+rl*(rl-rc)
    ratio_N=length<=1?1.0:(float(length)+1.0)/(float(length)-1.0)
    k_yz=0.34/(1.34+ratio_N)
    s_sq_daily=s_o_sq+k_yz*s_c_sq+(1.0-k_yz)*s_rs_sq
    var float EPSILON_YZV = 1e-10 // Consistent with VR's EPSILON_ATR
    var float raw_rma_val = 0.0
    var float e_comp_val = 1.0
    float smoothed_s_sq = na
    if not na(s_sq_daily)
        rma_alpha = 1.0 / float(length)
        if na(raw_rma_val[1]) and e_comp_val == 1.0 // First valid calculation for RMA
            raw_rma_val := s_sq_daily
        else
            raw_rma_val := (nz(raw_rma_val[1]) * (length - 1) + s_sq_daily) / length
        e_comp_val := (1.0 - rma_alpha) * e_comp_val
        smoothed_s_sq := e_comp_val > EPSILON_YZV ? raw_rma_val / (1.0 - e_comp_val) : raw_rma_val
    result = math.sqrt(math.max(0.0, nz(smoothed_s_sq)))
    result

// Inputs
i_length = input.int(20, title="Length", minval=1, tooltip="The lookback period for smoothing Yang-Zhang daily variance estimates.")

// Calculation
yzvValue = yzv(i_length)

// Plot
plot(yzvValue, title="YZV", color=color.yellow, linewidth=2)