https://en.wikipedia.org/wiki/Option_style#Difference_in_value "Obtaining a general formula for American options is one of finance's unsolved problems." There's no need for it Just use the BSM. And: https://money.stackexchange.com/que...ptions-worth-more-than-european-style-options "You can always sell the European option for more than the profit of exercising the American option. No benefit." by user1731, Jul 14, 2016 at 20:24 And: If possible (good Bid/Ask), then just simply close the option instead of exercising it, IMO.