3/2 Stochastic Volatility Proxy

This indicator, "3/2 Stochastic Volatility Proxy", implements a realized volatility model that incorporates advanced digital signal processing techniques, such as Butterworth filtering, super smoothing, RMS normalization, and optionally Z-Score transformation, to capture and visualize shifts in market volatility.

🔍 Indicator Overview: "3/2 Stochastic Volatility Proxy"
🎯 Purpose
To act as a momentum-based volatility proxy, estimating realized volatility and applying a 3/2 power transformation—a known mathematical volatility model—to better detect volatility regimes and potential price explosions or contractions.

📐 Core Mathematical Model: The 3/2 Stochastic Volatility Model
The 3/2 stochastic volatility model is defined in continuous time as:

🔑 Key Idea:
The variance follows a mean-reverting process, but the diffusion term has scaling. This makes the volatility more reactive to spikes, creating more realistic behavior for modeling risk, especially under high-volatility periods (tail events).

🧠 Indicator Components Explained
1. 🧮 Realized Variance Estimation
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ret = math.log(close / close[1]) // Log returns
vari = ta.sma(ret * ret, length) // Realized variance
volatility_proxy = math.pow(vari, 1.5) // Raise to 3/2 power
This transforms log returns into variance using a simple moving average.

The variance is then raised to the 3/2 power, per the 3/2 volatility model.

2. 🧹 Smoothing Options
Two smoothing techniques are available:

✅ Option 1: Z-Score Smoothing (Ehlers Loop logic)
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f_zscore(volatility_proxy, smoothing)
Normalizes the series to its statistical deviation from the mean.

Useful for spotting regime changes (e.g., +2σ or -2σ extremes).

✅ Option 2: RMS Scaled Filtering
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scaledFilt(volatility_proxy, ..., ..., ...)
This applies three steps:

Butterworth Highpass Filter → Removes slow drift, isolates cycles.

Super Smoother Filter → Reduces aliasing and short-term noise.

Fast RMS Normalization → Stabilizes the scale across varying regimes.

🛠 Filters and Utilities (Detailed)
🔸 butterworthHP()
A 2-pole high-pass filter that removes low-frequency trends to highlight cyclic components of volatility.

🔸 superSmoother()
Ehlers’ 2-pole smoother that attenuates high-frequency noise more effectively than EMA or SMA.

🔸 fastRMS()
An efficient way to estimate root mean square, normalizing the filtered signal to control amplitude.

📈 Plot and Alerts
🔸 plot(smoothed_vol)
Plots the smoothed, normalized volatility proxy:

Above 0 → Rising volatility.

Below 0 → Falling volatility.

Above +2σ / Below -2σ → Extreme volatility alerts.

🔸 Alert Conditions:
🔔 Cross Above 0 → Bullish volatility expansion.

🔔 Cross Below 0 → Bearish contraction or mean reversion.

🔔 Crossing ±2σ → Overheated or overcooled volatility zones.

🧪 Practical Use Cases
Volatility Momentum Proxy
Use this as a signal that volatility is accelerating (breakout environment).

Risk-on / Risk-off Filter
High values may warn of regime shifts; low values indicate calm markets.

Pair with Trend or Mean-Reverting Strategies
Helps determine if the current volatility favors breakouts or reversions.