// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("High-Low Volatility (HLV)", "HLV", overlay=false)

//@function Calculates High-Low Volatility based on the Parkinson number.
//@param length The period length for smoothing the Parkinson 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 High-Low Volatility value.
//@optimized for performance and dirty data
hlv(simple int length, simple bool annualize = true, simple int annualPeriods = 252) =>
    float lnH = math.log(high), float lnL = math.log(low)
    float C_4LN2_INV = 0.3606737602 // 1.0 / (4.0 * math.log(2.0))
    float parkinsonEstimator = C_4LN2_INV * math.pow(lnH - lnL, 2)
    var float raw_rma_parkinson = 0.0, var float e_rma = 1.0
    float rma_alpha = 1.0 / float(length)
    if not na(parkinsonEstimator)
        raw_rma_parkinson := na(raw_rma_parkinson[1]) ? parkinsonEstimator : (nz(raw_rma_parkinson[1], parkinsonEstimator) * (length - 1) + parkinsonEstimator) / 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_parkinson = e_rma > EPSILON and not na(raw_rma_parkinson) ? raw_rma_parkinson / (1.0 - e_rma) : raw_rma_parkinson
    float smoothedParkinsonEstimator = nz(corrected_rma_parkinson, parkinsonEstimator)
    float volatility = smoothedParkinsonEstimator < 0 ? na : math.sqrt(smoothedParkinsonEstimator)
    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 Parkinson 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
hlvValue = hlv(i_length, i_annualize, i_annualPeriods)

// Plot
plot(hlvValue, "HLV", color=color.yellow, linewidth=2)