"Pricing American options is an open problem in the quantitative finance. It has no closed form solution similar to the Black-Scholes formula for European options."
I'm fascinated by this. Why not? Is it some kind of regulation thing?
I'm fascinated by this. Why not? Is it some kind of regulation thing?
Other geographic naming styles for options are definitely more arbitrary; Asian options are called that simply because they were invented in Tokyo, for instance, rather than necessarily being particularly common in Asia. Meanwhile Bermuda and Canary options are called that because they're somewhere inbetween American and European options in terms of how they work; they have no real connection to Bermuda or the Canary islands.
IIRC, the coiners of those terms were American, and called the simpler type European as a snub.
Well, if nothing else, it should at least be easy to check that (even if they existed elsewhere earlier) Samuelson thought he was independently inventing these terms, right? Except, in the paper where he supposedly invented these terms [3], he introduces them as follows:
> However, the simple integral (24) does give a solution under all cases to the simpler case of a warrant that can be exercised only at the end of the period T. We might call this a "European warrant" by analogy with the "European call," which, unlike the American call that is exercisable at any time from now to T, is exercisable only at a specified terminal date.
Note that nowhere previously does the paper make use of the "American" or "European" terminology, so it sounds like "European call" and "American call" here are references to pre-existing terminology -- suggesting that he didn't invent it after all! Huh.
Well, that got murkier than I expected. Don't really want to investigate further right now, but sounds like he didn't actually invent the terminology after all...?
[1] https://www.macroption.com/american-vs-european-options/
[2] https://www.youtube.com/watch?v=RbIzwTGN3Yc&t=11m
[3] https://link.springer.com/chapter/10.1007/978-3-319-22237-0_...
Many big European companies have both American and European options available for them. I haven’t really seen any in the US (for individual stocks).
An American option should be priced assuming that the option is optimally exercised, otherwise this would create a soft arbitrage opportunity. The difficulty is determining when the option is optimally exercised because it depends on several potentially unknown and difficult to model factors.
Whereas American style option contracts can be exercised at any time up to the time of expiration.
The Black-Scholes formula is only applicable to European style option contracts.