Exactly as you said: you're guaranteed to buy to close only at the ask price, so this is actually your market value of your options.Quote from Option Trader:
Dividends make calls cheaper only if out-of-the-money. If in-the-money they should be more expensive because of the dividend, but that is true only for the ask price from my experience. Since you sell at bid you might get only a slight increase.
From McMillan's book:
strike = (1+rate)**time * (stock+put-call-dividend)
which may be approximated to:
put = strike + call - stock + dividend - interest_on_strike_amount
