// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Conditional Volatility (CV)", "CV", overlay=false)

//@function Calculates GARCH(1,1) conditional volatility
//@param length Initial period for parameter estimation
//@param alpha Weight on previous squared return
//@param beta Weight on previous variance
//@returns float Conditional volatility value
//@optimized for performance and efficient variance updating
cv(simple int length, simple float alpha, simple float beta) =>
    var float omega = 0.0
    var float longRunVar = 0.0
    var float prevVariance = 0.0
    float DAYS_IN_YEAR = 252.0
    float MIN_PRICE = 1e-10
    float DEFAULT_VARIANCE = 0.0001
    float safeClose = nz(close, close[1])
    safeClose := math.max(safeClose, MIN_PRICE)
    float safePrevClose = nz(close[1], close[2] != 0.0 ? close[2] : safeClose)
    safePrevClose := math.max(safePrevClose, MIN_PRICE)
    float logReturn = 0.0
    if safeClose > 0.0 and safePrevClose > 0.0
        logReturn := math.log(safeClose / safePrevClose)
    logReturn := math.abs(logReturn) > 0.2 ? math.sign(logReturn) * 0.2 : logReturn
    float squaredReturn = logReturn * logReturn
    if bar_index < length
        longRunVar := (bar_index * longRunVar + squaredReturn) / (bar_index + 1)
        prevVariance := longRunVar
    else if bar_index == length
        omega := (1.0 - alpha - beta) * longRunVar
        prevVariance := longRunVar
    float variance = nz(prevVariance, DEFAULT_VARIANCE)
    variance := omega + alpha * squaredReturn + beta * variance
    variance := math.max(variance, 0.0000001)
    prevVariance := variance
    math.sqrt(DAYS_IN_YEAR * variance) * 100
// ---------- Main loop ----------

// Inputs
i_length = input.int(20, "Length", minval=10, maxval=500, tooltip="Initial period for estimation")
i_alpha = input.float(0.2, "Alpha", minval=0.01, maxval=0.99, step=0.01, tooltip="Weight on previous squared return")
i_beta = input.float(0.7, "Beta", minval=0.01, maxval=0.99, step=0.01, tooltip="Weight on previous variance")

// Calculation
cvValue = cv(i_length, i_alpha, i_beta)

// Plot
plot(cvValue, "CV", color=color.yellow, linewidth=2)