# Technical Studies Reference

### Volume Zone Oscillator

This study calculates and displays the Volume Zone Oscillator of the Volume data.

Let $$V$$ and $$C$$ be random variables denoting the Volume and Closing Prices, respectively, and let $$V_t$$ and $$C_t$$ be their respective values Index $$t$$. We define a random variable $$R$$, called +/- Volume, whose value at Index $$t$$ is denoted as $$R_t$$. We calculate $$R_t$$ for $$t \geq 0$$ as follows.

For $$t = 0$$: $$R_0 = V_0$$

For $$t > 0$$: $$R_t = \displaystyle{\left\{ \begin{matrix} V_t & C_t > C_{t - 1} \\ -V_t & C_t \leq C_{t - 1} \end{matrix}\right .}$$

Let the Input Period be denoted as $$n$$. We denote the Volume Position and Total Volume at Index $$t$$ for the given Input as $$VP_t(n)$$ and $$TV_t(n)$$, respectively. We compute these in terms of Exponential Moving Averages as follows.

$$VP_t(n) = EMA_t(R,n)$$

$$TV_t(n) = EMA_t(V,n)$$

Finally, we denote the Volume Zone Oscillator for at Index $$t$$ for the given Input as $$VZO_t(n)$$, and we compute it for $$t \geq 0$$ and $$TV_t(n) \neq 0$$ as follows.

$$VZO_t(n) = \displaystyle{\frac{VP_t(n)}{TV_t(n)}}$$

This study also displays horizontal lines at levels determined by the Inputs Overbought Line1 Value, Overbought Line2 Value, Overbought Line3 Value, Oversold Line1 Value, Oversold Line2 Value, and Oversold Line3 Value.