# Barrier on realized volatility

I am trying to understand the risk exposures of vanilla options that also have a European barrier on realized volatility. For example, the option could knock out if the realized volatility over the time of the option exceeds a certain value (which could be set to be relatively low in order to cheapen the option). How would one do hedging for such instruments? How do risk exposures look like? Most of all, I am interested in understanding how such an instrument is influenced by the mean reversion speed, mean reversion level and especially by the (possibly time-dependent) volatility-of-variance.

Any reference would be much appreciated. Until now I could not find anything relevant, which is probably because I am using the wrong terms.

• I am not sure if you mean timer options, but if you do you should google "timer options" :) in particular the paper by Bernard and Cui. Here is the paper: papers.ssrn.com/sol3/papers.cfm?abstract_id=1612014 Mar 15 at 8:32
• @Frido I did not know about this product. It is similar, but still different. The payoff I am describing is not a continuously-monitored barrier. The barrier in my case is only observed at maturity, which means it is a simple indicator function with a condition that the realized vol over the entire duration of the product is above or below a certain level. Mar 15 at 8:43
• If you mean then the payoff function $$E_t [ (S_T - K)_+ \theta (L- V_{t,T}) ]$$ where $S_T$ is the terminal spot price and $\theta (L- V_{t,T})$ is the indicator function that realized variance over $[t,T]$ is less than $L$ then I need to think about it a bit more. The problem here is clearly that you need the joint distribution function. Mar 15 at 8:47
• I cannot honestly come up with a quick and dirty approximation yet for this. But take a look at the paper by Carr et al. which also discusses volatility hybrid derivatives. If all else fails: PDE or MC :) arxiv.org/abs/2107.00554 Mar 15 at 18:09
• The products are called vol knockout options (vko). I have no experience with them but there seems to be some results on Google. Mar 15 at 22:43