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. 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
I don't think that is true. Dividends always make a call cheaper even when the call is in the money. Of course, American style calls will not get any cheaper than parity. Here is the link posted by Def earlier. It makes no reference to ITM or OTM it just says that dividends make a call cheaper. http://www.investopedia.com/article...r/03/121003.asp
Excellent way to prove the dividend effect on Call prices. To make it clearer I have re-arranged your equation to reflect Call options (the subject of this discussion): Call = +stock-Strike +Put -dividend +interest_on_strike So it's clear that Calls are made cheaper because of the dividend.
Response to MoralHazard and DON87109 (for paragraph 2): American vs European style has to do with if options can be exercised before expiration. European style does not have the same dividend issue (except for at expiration). In-the-money calls should be worth more hypothetically, because people who have in-the-money puts with little time value left would stand to gain by paying more for in-the-money calls, as they can be exercised before ex-dividend date, and when the stock drops the next day, they don't lose, because they will exercise their puts. Someone mentioned the reason the calls don't may much more is because you also have to factor the time value they are sacraficing by exercising the puts early.