# Technical Studies Reference

### Volatility - Historical

This study calculates and displays the Historical Volatility for the data specified by the Input Data Input.

Let $$X$$ be a random variable denoting the Input Data Input. Then we denote the Logarithmic Return of the Input Data at Index $$t$$ as $$LR_t(X)$$, and we compute it for $$t > 0$$ as follows.

$$LR_t(X) = \displaystyle{\ln\left(\frac{X_t}{X_{t - 1}}\right)}$$

Let $$LR(X)$$ be a random variable denoting the Logarithmic Return of the Input Data, and let the Length and Number of Bars per Year Inputs be denoted as $$n$$ and $$N$$, respectively. Then we denote the Volatility - Historical at Index $$t$$ for the given Inputs as $$HVol_t(X,n,N)$$, and we compute it in terms of a Simple Moving Average for $$t \geq n$$ as follows.

$$HVol_t(X,n,N) = 100\displaystyle{\sqrt{N}\sqrt{\frac{1}{n - 1} \sum_{i = \max\{0,t-n+1\}}^t \left(LR_i(X) - SMA_t(LR(X),n)\right)^2}}$$

For an explanation of the Sigma ($$\Sigma$$) notation for summation, refer to our description here.

#### Inputs

• Input Data
• Length
• Number of Bars per Year: In order for this study to calculate historical volatility correctly, it is necessary for you to enter the number of bars in your chart that make up a one-year time period.