// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Garman-Klass Volatility (GKV)", "GKV", overlay=false)

//@function Calculates Garman-Klass Volatility.
//@param length The period length for smoothing the Garman-Klass estimator.
//@param annualize Boolean to indicate if the volatility should be annualized. Default is true.
//@param annualPeriods Number of periods in a year for annualization. Default is 252 for daily data.
//@returns float The Garman-Klass Volatility value.
//@optimized for performance and dirty data
gkv(simple int length, simple bool annualize = true, simple int annualPeriods = 252) =>
    if length <= 0
        runtime.error("Length must be greater than 0")
    if annualize and annualPeriods <= 0
        runtime.error("Annual periods must be greater than 0 if annualizing")
    float lnH = math.log(high), float lnL = math.log(low), float lnO = math.log(open), float lnC = math.log(close)
    float C_2LN2_1 = 0.3862941611 // 2 * math.log(2) - 1
    float term1 = 0.5 * math.pow(lnH - lnL, 2)
    float term2 = C_2LN2_1 * math.pow(lnC - lnO, 2)
    float gkEstimator = term1 - term2
    var float raw_rma_gk = 0.0, var float e_rma = 1.0
    float rma_alpha = 1.0 / float(length)
    if not na(gkEstimator)
        raw_rma_gk := na(raw_rma_gk[1]) ? gkEstimator : (nz(raw_rma_gk[1], gkEstimator) * (length - 1) + gkEstimator) / length
        e_rma := na(e_rma[1]) ? (1.0 - rma_alpha) : (1.0 - rma_alpha) * nz(e_rma[1], 1.0)
    float EPSILON = 1e-10
    float corrected_rma_gk = e_rma > EPSILON and not na(raw_rma_gk) ? raw_rma_gk / (1.0 - e_rma) : raw_rma_gk
    float smoothedGkEstimator = nz(corrected_rma_gk, gkEstimator)
    float volatility = smoothedGkEstimator < 0 ? na : math.sqrt(smoothedGkEstimator)
    annualize and not na(volatility) ? volatility * math.sqrt(float(annualPeriods)) : volatility

// ---------- Main loop ----------

// Inputs
i_length = input.int(20, "Length", minval=1, tooltip="Period for smoothing the Garman-Klass estimator")
i_annualize = input.bool(true, "Annualize Volatility", tooltip="Annualize the volatility output")
i_annualPeriods = input.int(252, "Annual Periods", minval=1, tooltip="Number of periods in a year for annualization (e.g., 252 for daily, 52 for weekly)")

// Calculation
gkvValue = gkv(i_length, i_annualize, i_annualPeriods)

// Plot
plot(gkvValue, "GKV", color=color.yellow, linewidth=2)