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This study calculates and displays a Synthetic VIX (Volatility Index) of the Price data.

Let \(L\) and \(C\) be random variables denoting the Low and Closing Prices, respectively, and let their respective values at Index \(t\) be \(L_t\) and \(C_t\). Let the Length Input be denoted as \(n\). We denote the Highest Close over a sliding window of Length \(n\) at Index \(t\) as \(\max_t(C,n)\), and we compute it for \(t \geq 0\) as follows.

We denote the Synthetic VIX at Index \(t\) for the given Input as \(SynthVIX_t(n)\), and we compute it for \(t \geq 0\) as follows.