QuanTAlib/docs/indicators/volatility/rvi/calc.md

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.