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volatility

Posted: December 2nd, 2019, 4:29 pm
by frolloos
Setting: Black-Scholes with deterministic volatility.

Vanilla options are priced with volatility equal to remaining variance/volatility [$] \int_t^T \sigma^2(u) du [$]. 

What kind of option, that is delta-hedgeable, has as input at current time [$] t [$] not the remaining variance, but the total variance [$] \int_0^T \sigma^2(u) du [$] from [$] u=0 [$] to [$]  u = T[$]?

See also my question here.

Is it a timer option that I should be looking at?

Re: volatility

Posted: December 2nd, 2019, 4:35 pm
by Alan
Ignoring the delta-hedgeable requirement, my thought was a capped variance swap, as the cap is triggered by the total variance. 

Re: volatility

Posted: December 2nd, 2019, 4:39 pm
by frolloos
Thanks - yes maybe that could work. Preferably I could somehow relate the instrument, whatever it is, to a single vanilla option (by eg choosing an appropriate strike), but I am starting to believe that may be impossible.