Black-Scholes Formula & American Option

[wailoon]

I have a question. Can Black-scholes formula apply to the American options? I came across a question in the text book asking me to compute the call price for European option using BS formula, followed by computing the call price for american option. How does that work? I thought BS formula can only be applied to European option?

[Defying Gravity]

If it's an American call on a non-dividend paying stock, then it's equal to a European call since it's never optimal to exercise early if you won't receive any dividends.

There could be other, more in-depth answers to your question--but I've found this to be a pretty common "trick" that's used by question writers.

[Actuarialsuck]

They might ask for bounds, so you can price a European call/put and then what would be the relation to its American counterpart?

[Force of Interest]

Originally Posted by wailoon

I have a question. Can Black-scholes formula apply to the American options? I came across a question in the text book asking me to compute the call price for European option using BS formula, followed by computing the call price for american option. How does that work? I thought BS formula can only be applied to European option?

I'm not sure if this applies to the question you are talking about, but there is a way to use the BS formula for an American call on a stock that pays a single discrete dividend. It involves compound options.

I actually need to go over that again so I can't really explain right now.

[scotth]

Originally Posted by wailoon

I have a question. Can Black-scholes formula apply to the American options?

Originally Posted by davidjstratton

I'm not sure if this applies to the question you are talking about, but there is a way to use the BS formula for an American call on a stock that pays a single discrete dividend. It involves compound options.

I actually need to go over that again so I can't really explain right now.

Absolutely. See ASM 5th Section 11.4.2 (14.4.2? 6th Edition)

If there is more than 1 discrete dividend, I'm not sure if it will use multiple compound options.

You can also calculate American options difference to a European option using a Monte Carlo simulation.