Volatility Risk Premium

// This Pine Script code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © EdgeTools
//
// Volatility Risk Premium (VRP)
// 
// Based on academic research:
// - Carr & Wu (2009): Variance Risk Premiums, Review of Financial Studies
// - Bollerslev, Tauchen & Zhou (2009): Expected Stock Returns and Variance Risk Premia
// - Bakshi & Kapadia (2003): Delta-Hedged Gains and the Negative Market Volatility Risk Premium
//
// The VRP measures the difference between implied volatility (VIX) and realized volatility.
// A positive VRP indicates investors pay a premium for volatility protection.
// Research shows VRP predicts future equity returns and signals market stress when negative.

//@version=6
indicator("Volatility Risk Premium", shorttitle="VRP", overlay=false, max_bars_back=5000)

// --- Inputs ---

// Core Settings
rv_length = input.int(20, "Realized Vol Period", minval=5, maxval=63, group="Core Settings")
rv_method = input.string("Close-to-Close", "RV Calculation Method", 
     options=["Close-to-Close", "Parkinson", "Garman-Klass"], group="Core Settings")
vrp_smoothing = input.int(5, "VRP Smoothing (EMA)", minval=1, maxval=21, group="Core Settings")
vrp_lookback = input.int(252, "Statistical Lookback", minval=60, maxval=1000, group="Core Settings")

// Regime Thresholds
threshold_high = input.float(5.0, "High VRP (%)", minval=1.0, maxval=15.0, step=0.5, group="Thresholds")
threshold_extreme = input.float(10.0, "Extreme VRP (%)", minval=5.0, maxval=20.0, step=0.5, group="Thresholds")
threshold_low = input.float(-2.0, "Low VRP (%)", minval=-10.0, maxval=2.0, step=0.5, group="Thresholds")

// Term Structure
rv_short = input.int(10, "Short-Term RV Period", minval=5, maxval=20, group="Term Structure")
rv_long = input.int(60, "Long-Term RV Period", minval=40, maxval=126, group="Term Structure")
show_term_structure = input.bool(false, "Show Term Structure Lines", group="Term Structure")

// Mean Reversion
mr_zscore_threshold = input.float(2.0, "Z-Score Threshold", minval=1.0, maxval=3.0, step=0.5, group="Mean Reversion")
show_mr_signals = input.bool(false, "Show MR Signals", group="Mean Reversion")
show_bollinger = input.bool(false, "Show VRP Bands", group="Mean Reversion")
bb_mult = input.float(2.0, "Band Multiplier", minval=1.0, maxval=3.0, step=0.5, group="Mean Reversion")

// Display
show_histogram = input.bool(true, "Histogram", group="Display")
show_line = input.bool(false, "Line", group="Display")
show_components = input.bool(false, "IV/RV Components", group="Display")
show_table = input.bool(true, "Statistics Panel", group="Display")
show_thresholds = input.bool(true, "Threshold Lines", group="Display")
show_background = input.bool(true, "Dynamic Background", group="Display")
color_candles = input.bool(true, "Color Candles", group="Display")
show_momentum = input.bool(false, "VRP Momentum", group="Display")
vrp_momentum_length = input.int(5, "Momentum Period", minval=1, maxval=20, group="Display")

// Appearance
color_scheme = input.string("EdgeTools", "Theme", 
     options=["EdgeTools", "Gold", "Ocean", "Fire", "Matrix", "Arctic"], group="Appearance")
use_dark_mode = input.bool(true, "Dark Mode", group="Appearance")
background_intensity = input.int(85, "Background Transparency", minval=70, maxval=95, step=5, group="Appearance")

// --- Color Definitions ---

color primary_color = switch color_scheme
    "EdgeTools" => use_dark_mode ? #3b82f6 : #2563eb
    "Gold" => use_dark_mode ? #FFD700 : #DAA520
    "Ocean" => use_dark_mode ? #20B2AA : #008B8B
    "Fire" => use_dark_mode ? #FF6347 : #DC143C
    "Matrix" => use_dark_mode ? #00FF41 : #006400
    "Arctic" => use_dark_mode ? #87CEFA : #4169E1
    => #3b82f6

color bullish_color = switch color_scheme
    "EdgeTools" => use_dark_mode ? #22c55e : #16a34a
    "Gold" => use_dark_mode ? #FFA500 : #FF8C00
    "Ocean" => use_dark_mode ? #00CED1 : #4682B4
    "Fire" => use_dark_mode ? #FFD700 : #FF8C00
    "Matrix" => use_dark_mode ? #39FF14 : #228B22
    "Arctic" => use_dark_mode ? #00BFFF : #0000CD
    => #22c55e

color bearish_color = switch color_scheme
    "EdgeTools" => use_dark_mode ? #ef4444 : #dc2626
    "Gold" => use_dark_mode ? #FF5252 : #D32F2F
    "Ocean" => use_dark_mode ? #FF4500 : #B22222
    "Fire" => use_dark_mode ? #8B0000 : #800000
    "Matrix" => use_dark_mode ? #FF073A : #8B0000
    "Arctic" => use_dark_mode ? #FF1493 : #8B008B
    => #ef4444

color neutral_color = switch color_scheme
    "EdgeTools" => use_dark_mode ? #737373 : #525252
    "Gold" => use_dark_mode ? #C0C0C0 : #808080
    "Ocean" => use_dark_mode ? #87CEEB : #2F4F4F
    "Fire" => use_dark_mode ? #FFA500 : #CD853F
    "Matrix" => use_dark_mode ? #00FFFF : #008B8B
    "Arctic" => use_dark_mode ? #B0E0E6 : #483D8B
    => #737373

color text_color = use_dark_mode ? #fafafa : #0a0a0a
color table_bg = use_dark_mode ? #171717 : #f9f9f9
color header_bg = use_dark_mode ? #262626 : #e5e5e5
table_transp = use_dark_mode ? 80 : 15

// --- Data Sources ---

vix = request.security("CBOE:VIX", timeframe.period, close, lookahead=barmerge.lookahead_off)

use_chart = syminfo.ticker == "SPY" or syminfo.ticker == "SPX" or syminfo.ticker == "ES1!"
spy_close = use_chart ? close : request.security("SPY", timeframe.period, close, lookahead=barmerge.lookahead_off)
spy_high = use_chart ? high : request.security("SPY", timeframe.period, high, lookahead=barmerge.lookahead_off)
spy_low = use_chart ? low : request.security("SPY", timeframe.period, low, lookahead=barmerge.lookahead_off)
spy_open = use_chart ? open : request.security("SPY", timeframe.period, open, lookahead=barmerge.lookahead_off)

// --- Realized Volatility Functions ---

log_ret = math.log(spy_close / nz(spy_close[1], spy_close))

calc_rv_ctc(int len) =>
    ta.stdev(log_ret, len) * math.sqrt(252) * 100

calc_rv_parkinson(int len) =>
    sum_sq = 0.0
    for i = 0 to len - 1
        if not na(spy_high[i]) and not na(spy_low[i]) and spy_low[i] > 0
            hl = math.log(spy_high[i] / spy_low[i])
            sum_sq += hl * hl
    math.sqrt(sum_sq / (4.0 * math.log(2.0) * len) * 252) * 100

calc_rv_gk(int len) =>
    sum_gk = 0.0
    for i = 0 to len - 1
        if not na(spy_high[i]) and not na(spy_low[i]) and not na(spy_open[i]) and not na(spy_close[i])
            if spy_low[i] > 0 and spy_open[i] > 0
                hl = math.log(spy_high[i] / spy_low[i])
                co = math.log(spy_close[i] / spy_open[i])
                sum_gk += 0.5 * hl * hl - (2 * math.log(2) - 1) * co * co
    math.sqrt(math.max(sum_gk / len, 0) * 252) * 100

get_rv(int len) =>
    switch rv_method
        "Close-to-Close" => calc_rv_ctc(len)
        "Parkinson" => calc_rv_parkinson(len)
        "Garman-Klass" => calc_rv_gk(len)
        => calc_rv_ctc(len)

// --- Core Calculations ---

realized_vol = get_rv(rv_length)
vrp_raw = vix - realized_vol
vrp = ta.ema(vrp_raw, vrp_smoothing)

// Statistics
vrp_mean = ta.sma(vrp, vrp_lookback)
vrp_stdev = ta.stdev(vrp, vrp_lookback)
vrp_zscore = (vrp - vrp_mean) / math.max(vrp_stdev, 0.001)
vrp_percentile = ta.percentrank(vrp, vrp_lookback)

// Term Structure
rv_short_val = get_rv(rv_short)
rv_long_val = get_rv(rv_long)
vrp_short = vix - rv_short_val
vrp_long = vix - rv_long_val
rv_slope = rv_long_val - rv_short_val

// Mean Reversion
vrp_upper = vrp_mean + bb_mult * vrp_stdev
vrp_lower = vrp_mean - bb_mult * vrp_stdev
mr_overbought = vrp_zscore >= mr_zscore_threshold
mr_oversold = vrp_zscore <= -mr_zscore_threshold
mr_long = mr_oversold and vrp > nz(vrp[1])
mr_short = mr_overbought and vrp < nz(vrp[1])

// Momentum
vrp_roc = vrp - nz(vrp[vrp_momentum_length])

// Regime
var int regime_bars = 0
var string last_regime = "NORMAL"

get_regime() =>
    if vrp >= threshold_extreme
        "EXTREME"
    else if vrp >= threshold_high
        "HIGH"
    else if vrp >= 0
        "NORMAL"
    else if vrp >= threshold_low
        "LOW"
    else
        "NEGATIVE"

regime = get_regime()
regime_change = regime != last_regime
regime_bars := regime_change ? 1 : regime_bars + 1
last_regime := regime

// --- Dynamic Colors ---

get_vrp_color() =>
    if vrp >= threshold_extreme
        color.from_gradient(vrp, threshold_extreme, threshold_extreme + 5, bullish_color, primary_color)
    else if vrp >= threshold_high
        bullish_color
    else if vrp >= 0
        color.from_gradient(vrp, 0, threshold_high, neutral_color, bullish_color)
    else if vrp >= threshold_low
        color.from_gradient(vrp, threshold_low, 0, bearish_color, neutral_color)
    else
        bearish_color

vrp_color = get_vrp_color()

get_bg_color() =>
    if vrp >= threshold_extreme
        color.from_gradient(vrp, threshold_extreme, threshold_extreme + 5, primary_color, bullish_color)
    else if vrp >= threshold_high
        color.from_gradient(vrp, threshold_high, threshold_extreme, bullish_color, primary_color)
    else if vrp >= 0
        color.from_gradient(vrp, 0, threshold_high, neutral_color, bullish_color)
    else if vrp >= threshold_low
        color.from_gradient(vrp, threshold_low, 0, bearish_color, neutral_color)
    else
        bearish_color

get_bg_opacity() =>
    abs_v = math.abs(vrp)
    max_ex = math.max(math.abs(threshold_extreme), math.abs(threshold_low))
    if abs_v >= max_ex
        int(math.max(70, math.min(75, 70 + (abs_v - max_ex) * 2)))
    else if abs_v >= threshold_high
        int(math.max(80, math.min(85, 80 + (abs_v - threshold_high))))
    else
        background_intensity

// --- Plotting ---

bgcolor(show_background ? color.new(get_bg_color(), get_bg_opacity()) : na, title="Background")
barcolor(color_candles ? vrp_color : na, title="Candles")

plot(show_histogram ? vrp : na, "VRP", vrp_color, style=plot.style_histogram, linewidth=3)
plot(show_line ? vrp : na, "VRP Line", vrp_color, linewidth=2)

hline(0, "Zero", color.new(neutral_color, 50))
plot(show_thresholds ? threshold_high : na, "High", color.new(bullish_color, 60))
plot(show_thresholds ? threshold_extreme : na, "Extreme", color.new(primary_color, 60))
plot(show_thresholds ? threshold_low : na, "Low", color.new(bearish_color, 60))

plot(show_components ? vix : na, "VIX", color.new(primary_color, 40))
plot(show_components ? realized_vol : na, "RV", color.new(bearish_color, 40))

plot(show_bollinger ? vrp_upper : na, "Upper Band", color.new(bullish_color, 70))
plot(show_bollinger ? vrp_lower : na, "Lower Band", color.new(bearish_color, 70))
plot(show_bollinger ? vrp_mean : na, "Mean", color.new(neutral_color, 50))

plotshape(show_mr_signals and mr_long, title="Buy", location=location.bottom, style=shape.triangleup, size=size.small, color=bullish_color)
plotshape(show_mr_signals and mr_short, title="Sell", location=location.top, style=shape.triangledown, size=size.small, color=bearish_color)

plot(show_term_structure ? vrp_short : na, "VRP Short", color.new(primary_color, 50))
plot(show_term_structure ? vrp_long : na, "VRP Long", color.new(neutral_color, 50))

mom_col = vrp_roc > 0 ? color.new(bullish_color, 60) : color.new(bearish_color, 60)
plot(show_momentum ? vrp_roc : na, "Momentum", mom_col, style=plot.style_histogram, linewidth=2)

// --- Statistics Panel ---

if show_table and barstate.islast
    var tbl = table.new(position.top_right, 2, 12, border_width=1, bgcolor=color.new(table_bg, table_transp))
    table.clear(tbl, 0, 0, 1, 11)
    
    table.cell(tbl, 0, 0, "VRP Analysis", text_color=text_color, bgcolor=color.new(header_bg, 20), text_size=size.small)
    table.cell(tbl, 1, 0, "", bgcolor=color.new(header_bg, 20))
    
    table.cell(tbl, 0, 1, "VRP", text_color=text_color, text_size=size.small)
    table.cell(tbl, 1, 1, str.tostring(vrp, "#.##") + "%", text_color=vrp_color, text_size=size.small)
    
    table.cell(tbl, 0, 2, "VIX", text_color=text_color, text_size=size.small)
    table.cell(tbl, 1, 2, str.tostring(vix, "#.##") + "%", text_color=color.new(primary_color, 40), text_size=size.small)
    
    table.cell(tbl, 0, 3, "Realized Vol", text_color=text_color, text_size=size.small)
    table.cell(tbl, 1, 3, str.tostring(realized_vol, "#.##") + "%", text_color=color.new(bearish_color, 40), text_size=size.small)
    
    reg_col = regime == "EXTREME" ? primary_color : regime == "HIGH" ? bullish_color : regime == "NORMAL" ? neutral_color : bearish_color
    table.cell(tbl, 0, 4, "Regime", text_color=text_color, text_size=size.small)
    table.cell(tbl, 1, 4, regime, text_color=reg_col, text_size=size.small)
    
    table.cell(tbl, 0, 5, "Duration", text_color=text_color, text_size=size.small)
    table.cell(tbl, 1, 5, str.tostring(regime_bars) + " bars", text_color=neutral_color, text_size=size.small)
    
    pct_col = vrp_percentile > 70 ? bullish_color : vrp_percentile < 30 ? bearish_color : neutral_color
    table.cell(tbl, 0, 6, "Percentile", text_color=text_color, text_size=size.small)
    table.cell(tbl, 1, 6, str.tostring(vrp_percentile, "#.#") + "%", text_color=pct_col, text_size=size.small)
    
    z_col = vrp_zscore > 1 ? bullish_color : vrp_zscore < -1 ? bearish_color : neutral_color
    table.cell(tbl, 0, 7, "Z-Score", text_color=text_color, text_size=size.small)
    table.cell(tbl, 1, 7, str.tostring(vrp_zscore, "#.##"), text_color=z_col, text_size=size.small)
    
    slope_col = rv_slope > 0 ? bullish_color : bearish_color
    table.cell(tbl, 0, 8, "RV Slope", text_color=text_color, text_size=size.small)
    table.cell(tbl, 1, 8, str.tostring(rv_slope, "#.##") + "%", text_color=slope_col, text_size=size.small)
    
    mom_tbl_col = vrp_roc > 0 ? bullish_color : bearish_color
    table.cell(tbl, 0, 9, "Momentum", text_color=text_color, text_size=size.small)
    table.cell(tbl, 1, 9, str.tostring(vrp_roc, "#.##"), text_color=mom_tbl_col, text_size=size.small)
    
    mr_txt = mr_overbought ? "OVERBOUGHT" : mr_oversold ? "OVERSOLD" : "NEUTRAL"
    mr_col = mr_overbought ? bearish_color : mr_oversold ? bullish_color : neutral_color
    table.cell(tbl, 0, 10, "MR Status", text_color=text_color, text_size=size.small)
    table.cell(tbl, 1, 10, mr_txt, text_color=mr_col, text_size=size.small)
    
    bias_txt = vrp > threshold_high ? "RISK-ON" : vrp < 0 ? "RISK-OFF" : "NEUTRAL"
    bias_col = vrp > threshold_high ? bullish_color : vrp < 0 ? bearish_color : neutral_color
    table.cell(tbl, 0, 11, "Bias", text_color=text_color, text_size=size.small)
    table.cell(tbl, 1, 11, bias_txt, text_color=bias_col, text_size=size.small)

// --- Alerts ---

alertcondition(vrp >= threshold_extreme, "Extreme VRP", "VRP extreme high - elevated risk aversion")
alertcondition(vrp >= threshold_high and vrp < threshold_extreme, "High VRP", "VRP above normal - risk premium elevated")
alertcondition(vrp < threshold_low, "Negative VRP", "VRP negative - realized exceeds implied (stress)")
alertcondition(ta.cross(vrp, 0), "Zero Cross", "VRP crossed zero line")
alertcondition(math.abs(vrp_zscore) > 2, "Z-Score Extreme", "VRP statistically extreme")
alertcondition(mr_long, "MR Buy Signal", "VRP mean reversion buy signal")
alertcondition(mr_short, "MR Sell Signal", "VRP mean reversion sell signal")
alertcondition(ta.crossunder(rv_slope, 0), "Term Structure Inversion", "Short-term RV exceeds long-term (stress)")
alertcondition(ta.crossover(rv_slope, 0), "Term Structure Normal", "Term structure normalized")
alertcondition(regime_change, "Regime Change", "VRP regime changed")