Historical Volatility

The historical volatility is simply the standard deviation of the Index Total Returns $//<![CDATA[ \begin{array}{l}TR_t\end{array} //]]>$ within a certain time period. 

It is given by:

$$//<![CDATA[ \begin{array}{l}\displaystyle Vol = \sqrt{\frac{\sum_{t=1}^T (TR_t - \bar{TR})^2}{T-1}}\end{array} //]]>$$

where   $//<![CDATA[ \begin{array}{l}TR_t\end{array} //]]>$ is the index total return at time  $//<![CDATA[ \begin{array}{l}t\end{array} //]]>$ and  $//<![CDATA[ \begin{array}{l}\bar{TR}\end{array} //]]>$ is the mean total return over period . $//<![CDATA[ \begin{array}{l}T\end{array} //]]>$