answer a financial math question

[Kuciwalker]

Given a non-dividend-paying stock and a risk-free rate of 0%, why is the price of an American and European option with the same strike price and expiration date the same?

It sort of makes sense to me that this is true, but I can't construct a convincing proof of it.

[Hauldren Collider]

why would a stock have value if it doesn't pay dividends

[Kuciwalker]

Beside the point.

[Jon Miller]

Partial ownership/etc?

JM

[Japher]

why wouldn't it be?

[Kuciwalker]

Oh I figured it out.

from Pt = (K - St)*D(T-t) + Ct
D(T-t) = 1 => Pt > K - St = return from exercising option => you will never exercise option => European and American options are identical

[Hauldren Collider]

Cue Ben saying "I couldn't find the error, try factoring the integrand!"

[Flubber]

Given a non-dividend-paying stock and a risk-free rate of 0%, why is the price of an American and European option with the same strike price and expiration date the same?

It sort of makes sense to me that this is true, but I can't construct a convincing proof of it.

I confess I did not quite understand your question. Are you talking about a hypothetical single stock denominated in both US dollars and Euros??

[Flubber]

why would a stock have value if it doesn't pay dividends

I hope you are joking

[Japher]

I have about a total of 2 stocks in portfolio that pay dividens (or rather have in the past couple of years) and I certainly hope they are worth something

[Hauldren Collider]

I hope you are joking

I wasn't joking. I don't know very much at all about financial math. It was an honest question. However I have since figured it out.

[Kuciwalker]

I confess I did not quite understand your question. Are you talking about a hypothetical single stock denominated in both US dollars and Euros??

American option = can be exercised any time before the expiration date
European option = can only be exercised on the expiration date

[N35t0r]

stock = stock option?

[Flubber]

American option = can be exercised any time before the expiration date
European option = can only be exercised on the expiration date

hmmm I had not seen that term before

As described, for almost any given stock in the real world, the American option would be one that investors should prefer and therefore value more highly (if for example we are talking a purchase option at some strike price above the market price on the day the option is issued. ) I would much prefer to have x days in which the exercise of my option may be worth something compared to a single opportunity on the expiration date

[Kuciwalker]

Obviously the price of an American option is at least the price of the European option. The point is that if the interest rate is 0 and there are no dividends, it turns out that you never exercise the American option before the expiration so they are the same.

No offense, but I'm pretty sure this math is beyond your training and you couldn't have actually helped me.