# Does the Asian Option (average Option) depend on the forward implied vol

I can easily understand that the forward starting Option and Barrier Option depend on the forward implied vol smile at resetting date, so we always choose the stochastic vol model for underlying to control the forward vol.

Does the Asian Option (discrete arithmetic araverage) also depend on the forward implied vol? And it seems each path dependent Option depends on the forward implied vol.

Can anyone give me a clear explaination?

• First, I presume you mean a continuously observed barrier option? And second, I would say that you can have path dependence without forward vol dependence if each of the observations are independent. That's not a required property, but just intuitively and only thinking for a few minutes it seems like it could be sufficient. – will Dec 9 '18 at 9:58
• @will 1. I think even there is only one observed point of barrier option, it still depends on the forward vol (vol smile at observation point). 2. How do you define independent obseevation? Is Asian option independent observations? Since observation $S_{T_2}$ will depend on the observation value $S_{T_1}$ and the vol smile at $T_1$ if $T_2>T_1.$ – user6703592 Dec 9 '18 at 10:17
• if the barrier observation. Is the same as the option expiry then the price can be replicated using vanillas and you don't need information on the forward/conditional volatility. – will Dec 11 '18 at 6:48