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