Using the recombining tree model as described in Haug's Option Pricing Forumla one can factor in multiple future discrete dividends when calculating the option value and greeks.
What's unclear is how does one handle a stock that pays a regular quarterly dividend but has only declared (as is standard) the next quater's dividend. If the option expires in one year, the next dividend is know, but the remaining three dividends have not yet been declared.
Should one use past dividends as a reference?
Do you only use the [single] declared dividend (even though it's assumed there will be 4 dividends during the life of the option)?
My assumption is they you'd plug in the known and use the past dates / amounts as a reference for the other 'future' dividends' and revise those with the actual information when they are finally declared, but that's only an assumption.