Historical Volatility with HV Average & High/Low Trendlines

### 📊 **Indicator Title**: Historical Volatility with HV Average & High/Low Trendlines

**Version**: Pine Script v5
**Purpose**:
This script visualizes market volatility using **Historical Volatility (HV)** and enhances analysis by:

* Showing a **moving average** of HV to identify volatility trends.
* Marking **high and low trendlines** to highlight extremes in volatility over a selected period.

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### 🔧 **Inputs**:

1. **HV Length (`length`)**:
Controls how many bars are used to calculate Historical Volatility.
*(Default: 10)*

2. **Average Length (`avgLength`)**:
Number of bars used for calculating the moving average of HV.
*(Default: 20)*

3. **Trendline Lookback Period (`trendLookback`)**:
Number of bars to look back for calculating the highest and lowest values of HV.
*(Default: 100)*

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### 📈 **Core Calculations**:

1. **Historical Volatility (`hv`)**:

$$
HV = 100 \times \text{stdev}\left(\ln\left(\frac{\text{close}}{\text{close}[1]}\right), \text{length}\right) \times \sqrt{\frac{365}{\text{period}}}
$$

* Measures how much the stock price fluctuates.
* Adjusts annualization factor depending on whether it's intraday or daily.

2. **HV Moving Average (`hvAvg`)**:
A simple moving average (SMA) of HV over the selected `avgLength`.

3. **HV High & Low Trendlines**:

* `hvHigh`: Highest HV value over the last `trendLookback` bars.
* `hvLow`: Lowest HV value over the last `trendLookback` bars.

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### 🖍️ **Visual Plots**:

* 🔵 **HV**: Blue line showing raw Historical Volatility.
* 🔴 **HV Average**: Red line (thicker) indicating smoothed HV trend.
* 🟢 **HV High**: Green horizontal line marking volatility peaks.
* 🟠 **HV Low**: Orange horizontal line marking volatility lows.

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### ✅ **Usage**:

* **High HV**: Indicates increased risk or potential breakout conditions.
* **Low HV**: Suggests consolidation or calm markets.
* **Cross of HV above Average**: May signal rising volatility (e.g., before breakout).
* **Touching High/Low Levels**: Helps identify volatility extremes and possible reversal zones.