# Technical Studies Reference

### Synthetic VIX

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.

$$\max_t(C,n) =\left\{ \begin{matrix} \max\{C_0,...,C_t\} & t < n - 1 \\ \max\{C_{t - n + 1},...,C_t\} & t \geq n - 1 \end{matrix}\right .$$

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.

$$SynthVIX_t(n) = \displaystyle{100 \cdot \frac{\max_t(C,n) - L_t}{\max_t(C,n)}}$$