2
$\begingroup$

Can someone give me an explanation of what integrated volatility is (and possibly why it is preferred) versus a standard measure of volatility eg variance?

$\endgroup$
4
$\begingroup$

In a standard approach you would think about the evolution of a return process in the following form: $$dr_t=\mu dt+\sigma dW_t,$$ where for the sake of simplicity I assumed constant volatility and drift ($\mu$ and $\sigma$ can also depend on the time parameter $t$). Often you will be interested into the variance of your stock returns (for example to hedge your risks, quantify your exposure to risk or for portfolio optimization) during a certain time period $[\tau,\tau-h]$. Standard Itô Calculus gives you that the 'aggregated' volatility over this time interval is just $$\int_\tau ^{\tau-h}\sigma^2 dt.$$ This term is called integrated variance and can be estimated via the sum of squared returns during this period (this gives you the close connection to realized volatility.

$\endgroup$
  • 2
    $\begingroup$ I would add: If you think about the BS formula, the variance $\sigma^2$ never appears by itself but always in conjunction with $T$. Those terms $\sigma^2 T$ represent in a sense the integrated volatility for the constant vol case. If you believe that vol is subject to change in a deterministic fashion, you could replace those terms with whatever integ vola you think appropriate. $\endgroup$ – Alex C Jan 29 '16 at 0:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.