Pricing Americans with finite-difference
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Pricing Americans with finite-difference
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Re: Pricing Americans with finite-difference
#2I'd rename "Americans" to "American options" for clarity.
Re: Pricing Americans with finite-difference
#3"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?
Re: Pricing Americans with finite-difference
#4"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 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.
Re: Pricing Americans with finite-difference
#5"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?
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.
Re: Pricing Americans with finite-difference
#6"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?
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.
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.
Re: Pricing Americans with finite-difference
#7"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 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 ca…
> 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.
Re: Pricing Americans with finite-difference
#8"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?
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.
Why does having variable duration mean an equation cannot model this type of option?
Re: Pricing Americans with finite-difference
#9This method will work but will require a large grid and consequently be quite slow. And order of magnitude or two faster than this is possible if you are clever.
Re: Pricing Americans with finite-difference
#10Earlier quoted context omitted.
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.
Why does having variable duration mean an equation cannot model this type of option?
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)