The typical kind of contracts are options on dividend futures.
https://www.eurex.com/ex-en/markets/did ... ons-946274
In this case the underlying is simply a future, and there is no need for an assumption of the individual future dividends, unless we price the front month.
For the front month, the theoretical vol should indeed decrease close to expiry (since most of the dividends are known) and using some sort of Asian approx may make sense. That being said, if you hedge your option with futures, using a simple term structure of vols would likely be good enough.