RVI

docs/indicators/volatility/rvi/calc.md

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+# The Math Behind RVI
+
+## Components of RVI
+
+The **Relative Volatility Index (RVI)** measures the direction of volatility in the market, using components like:
+
+- Standard deviation of price changes
+- Simple moving average (SMA) to smooth volatility
+- Separation of up and down price movements
+
+### RVI Formula
+
+The RVI is calculated using the following formula:
+
+$$
+\text{RVI}_t = 100 \times \frac{\text{SMA}(\sigma_{\text{up}}, N)}{\text{SMA}(\sigma_{\text{up}}, N) + \text{SMA}(\sigma_{\text{down}}, N)}
+$$
+
+Where:
+- \( \text{RVI}_t \) is the RVI value at time \( t \)
+- \( \sigma_{\text{up}} \) is the standard deviation of up moves over the lookback period \( N \)
+- \( \sigma_{\text{down}} \) is the standard deviation of down moves over the lookback period \( N \)
+- \( \text{SMA} \) represents the simple moving average applied over \( N \) periods
+
+### Up and Down Move Calculation
+
+The standard deviations \( \sigma_{\text{up}} \) and \( \sigma_{\text{down}} \) are calculated based on the price changes:
+
+$$
+\Delta \text{Price} = \text{Close}_t - \text{Close}_{t-1}
+$$
+
+- If \( \Delta \text{Price} > 0 \), it contributes to \( \sigma_{\text{up}} \)
+- If \( \Delta \text{Price} < 0 \), it contributes to \( \sigma_{\text{down}} \)
+
+### Parameter Definitions
+
+RVI uses the following main parameters:
+
+- **Lookback period** (\( N \)): The number of periods used to calculate the standard deviations and SMAs. A typical value is 14.
+- **Smoothing with SMA**: The standard deviations of up and down moves are smoothed using a simple moving average (SMA), making the RVI less sensitive to short-term fluctuations.
+
+### Computational Process
+
+For each new data point:
+- Calculate the price change (\( \Delta \text{Price} \)) from the previous period.
+- Separate the price changes into up moves and down moves.
+- Compute the standard deviations (\( \sigma_{\text{up}} \) and \( \sigma_{\text{down}} \)) over the last \( N \) periods.
+- Apply the simple moving average (SMA) to both up and down standard deviations.
+- Use the RVI formula to produce the final RVI value.