answer a financial math question

[Flubber]

stock = stock option?

No options are just that -- oppptunities to buy or sell stock within a specified time period at a set price.

You may pay 50 cents a share for an option to buy ABC company 6 months from now at 105 dollars a share (currently trading at 100 dollars a share)

If 6 months from now the stock is trading at 105 or less you lost your 50 cents. If its trading at 105.50 you can exercise and then sell to break even (less commissions of course LOL).

People buy options as a means to participate in the upside or downside of a stock without having to invest the full stock price.


Options are also sometime given to employees as a long term incentive program so that we participate in the growth of the value of the company. My employer gives all employees option with the strike price being the actual market price on the day of grant but they don't vest for a number of years. But if the stock price goes up at all they represent a potential pot of money and therefore a reason NOT to leave your employer (If you resign all unvested and unexercised options are forfeit).

For an employee its an interesting game-- If my options today can be exercised at a gain of 3.00 a share, do I do that now or do hope the share price goes up again between now and expiry. For me I REALLY start thinking about that when an option has a year to go. People that hang on to the end can get shafted (recent recession anyone) and see no value from an option which would have been valuable at several points prior in time HAD THEY EXERCISED IT.

[N35t0r]

I know the difference between an option and what it was the option of (I do some agri products' futures), its just that the OP didn't mention option actually it did, I missed it.

[Flubber]

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

No offense taken-- An accurate assement of my math skills-- I was more interested in the realities of your example than the math anyway

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.

If we are talking options in common stock , there may be many opportunities where a real investor might exercise early based on an assessment of the company, industry trends or even recent events. The American option holder may have the chance to exerercie and sell a stock for gain while the European option holder finds no value in the exercise as the stock goes back down prior to expiry.

In fact your assessment that you never exercise an option before expiry day would be true only for stable or rising stocks (if you have a purchase option)

[Japher]

That would depend if it's a call or put option.

Regardless, someone might sell a call option based purely on the timing of their investments rather than the movement of the stock, forcing them to exercise prior to the expiration date.

[Ben Kenobi]

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

I'm a physicist, not an economist!

[Kuciwalker]

If we are talking options in common stock , there may be many opportunities where a real investor might exercise early based on an assessment of the company, industry trends or even recent events. The American option holder may have the chance to exerercie and sell a stock for gain while the European option holder finds no value in the exercise as the stock goes back down prior to expiry.

In fact your assessment that you never exercise an option before expiry day would be true only for stable or rising stocks (if you have a purchase option)

Under a bunch of assumptions you can show that the present value of the American option is always greater than the money you could earn by exercising it, when the stock pays no dividends and the risk-free rate is 0, i.e. no rational investor would exercise the option prior to expiration.

Obviously, several of these assumptions aren't actually true. They are useful mathematical constructs.

[KrazyHorse]

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.

Use Jensen's inequality and the fact that under the risk-free measure the price of the stock is a martingale.

[KrazyHorse]

I'm a physicist, not an economist!

You're not a physicist, you piece of ****.

[Hauldren Collider]

I probably know more physics than Ben Kenobi

[KrazyHorse]

If we are talking options in common stock , there may be many opportunities where a real investor might exercise early based on an assessment of the company, industry trends or even recent events. The American option holder may have the chance to exerercie and sell a stock for gain while the European option holder finds no value in the exercise as the stock goes back down prior to expiry.

In fact your assessment that you never exercise an option before expiry day would be true only for stable or rising stocks (if you have a purchase option)

/

This post is utterly ridiculous. I suggest you read a basic financial math book. Real investors, if they wish to take a market view, will resell the option for >= the intrinsic value in the market (strictly greater if implied volatility is anything other than 0). If the price was ever less than the intrinsic value then there exists a simple arbitrage. Exercising early is always suboptimal, modulo transaction costs and some minor difficulties like shorting at a retail level.

[Ben Kenobi]

You're not a physicist, you piece of ****.

Dammit, KH!

[Ecofarm]

That's physician.

[Ben Kenobi]

I probably know more physics than Ben Kenobi

No. You're in what, HS?

Do two years and you'll have the same.

[Hauldren Collider]

No. You're in what, HS?

Do two years and you'll have the same.

I've taken college level physics you dumb ****

[Ben Kenobi]

Gee what a surprise. So have I. Two years.

Do two years of Physics and you'll have the same.