[hiAndrewQuinn]

"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?

[Sniffnoy]

I think you've misunderstood the terminology a bit. "European options" and "American options" don't mean "options in Europe" and "options in America"; they're just names for two different styles of options. I assume there is some real geographic origin to the naming convention, but I'm pretty sure both exist in both places.

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.

[twic]

> I assume there is some real geographic origin to the naming convention, but I'm pretty sure both exist in both places.

IIRC, the coiners of those terms were American, and called the simpler type European as a snub.

[Sniffnoy]

Hm, looking into it, I'm having trouble finding an easy answer. A quick search turned up this article [1] which says that yes Paul Samuelson named it that way for that reason, and links to this video [2] where he claims exactly that. But it also links to a source suggesting that the terms might predate Samuelson and be geographic in origin after all.

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_...

[ravetcofx]

Maybe Think of American options like concert tickets that you can use anytime before the show. Unlike tickets that only work on the day of the event (like European options), these tickets (American options) can be used whenever you want. Figuring out their price is tricky because you need to consider when it's best to use them, making it harder to have a simple formula like we do for tickets with fixed dates.

[Sniffnoy]

Sorry, did you mean to reply to a different comment? This doesn't appear related to what I was discussing (the etymology of the terms; I'm aware of what they mean).

[Reviving1514]

This is really well researched and I enjoyed following along, thank you.

[ffgjgf1]

> but I'm pretty sure both exist in both places.

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).

[hiAndrewQuinn]

Thanks!

[leplen]

American options can be exercised at any time at the investor's discretion. This means the instrument has a maximum duration, but the actual duration is up to choice of the option holder, which you can't model with an equation.

[auc]

This is subtly incorrect.

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.

[l33t7332273]

Why does having variable duration mean an equation cannot model this type of option?

[hfhdjdks]

The point is not whether it can be modeled (it can), but whether you can get a closed form solution for it (you can't...or we don't know how for now)

[gituliar]

As already mentioned American / European / Bermuda / Asian options vary by features of option contracts. They don't belong to a particular regulatory regime. For some reason its names are associated to the geo locations. I'm sure there are people who can wrap that in a nice narrative. :)

[sheepscreek]

European style option contracts are exercisable/allocated only at the time of expiration.

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.