# Technical Studies Reference

### HL Volatility

This study calculates and displays a HL Volatility indicator for the Price Data.

Let $$H$$, $$L$$, and $$C$$ be random variables denoting the High, Low, and Close Prices, and let $$H_t$$, $$L_t$$, and $$C_t$$ be their respective values at Index $$t$$. Let the Moving Average Length Input be denoted as $$n$$. We begin by computing $$HLDiff_t(n)$$, the difference between the Highest High and Lowest Low, as follows.

$$HLDiff_t(n) = \max_t(H,n) - \min_t(L,n)$$

We denote the HL Volatility as $$HLVol_t(n)$$, and we compute it for $$t > 0$$ in terms of Exponential Moving Averages as follows.

$$\displaystyle{HLVol_t(n) =\left\{ \begin{matrix} 100\cdot\frac{EMA_t(HLDiff(n),n)}{EMA_t(C,n)} & EMA_t(C,n) \neq 0 \\ 0 & EMA_t(C,n) = 0 \end{matrix}\right .}$$

Note: Depending on the setting of the Input Moving Average Type, the Exponential Moving Averages in each of the above formulas could be replaced with Linear Regression Moving Averages, Simple Moving Averages, Weighted Moving Averages, Wilders Moving Averages, Simple Moving Averages - Skip Zeros, or Smoothed Moving Averages.