Hi, I am struggling to understand why american call option is only worth as much as a european call option. If the call option is deep in the money, why is it not beneficial to have the option to exercise early? Thanks
Think you get them mixed up. SHould be the other way around. American call is always worth at least as much as European call.
Agree with elcfa… American call is always worth at least as much or more than an European Call Option. Hint; Rember that increased volitility increases the value of an option ie. longer time frame=greater volitilty (Think same concept as Bonds, Longer time frame=greater volitilty=greater required return. In other words increased volitility always demands greater payouts)…plus an American Option can be exercised at anytime, in other words its gains could captured at anytime, where the European Option in the same sceanario would need to hold it’s value in order to capture those gains on the strike date. Increased volitility increases the value of options and American Options benefit the most from increased volitility, hence American Options will always be > or = to the Value of a European Option.
Since an American option is always greater than the European option it would be worth more to sell the option then exercise it…It could be worth exercising early however, if the option pays a dividend
In general, American options are worth atleast as much as Europian Options, because they can be exercised earlier. But, for an American Call option, (on a non-dividend paying stock), it will be worth as much as a Europian Call option. Logic is, though you can exercise your call early, but then you have to pay up early too. Meaning you have to part from your cash earlier and thus loose any interest earning opportunity on that cash. So, the payoff is better, if you keep your cash till the expiration date and exercise your option on the exercise date. So, you are exercising it the same way as a Europian option. The thumb rule is: 1) When you have to part from your cash, you delay it as much as possible (like in exercising a call option) and 2) When you have to receive cash, you do it sooner rather than later (like in exercising a put option) Hope it helps.
Thanks for the replies guys. I did not get them mixed up. From what I read, american call option = european call option. But I thought that american call option should be > european call option because of the flexibility to exercise early. I think I might be confused by the fact that an early exercise might not mean exercise and sell. Can you exercise and sell american option before expiration? Can you do the same for european option? Thanks in advance.
provided there is liquidity in the market you can sell any option before expiration. but only the american option can be exercised early.
Wouldn’t the minimum value for the American option be the (underlying px - strike px) * risk free rate ^ time to expiration?
d31dy Wrote: >american > call option should be > european call option > because of the flexibility to exercise early. american call option >= european call option The > happens when there is underlying cashflow that make it worthwhile (i.e., give return > opportunity cost) for the cash (strike price) you have to ante to own the asset (which give you the cashflow before expiration date). In this case, it pays for you to own the asset before expiration date --> American option more worth. A big assumption here is that the option in in the money when you choose to exercise it, otherwise, it is of course cheaper to buy the asset at market price. Otherwise, it is like the book points out: “like renewing a magazine subscription before current subscription expires. Not only do you lose the interest on the money, you also lose the right to decide later if you want to renew.” In this case, there is no incentive to hurry to exercise --> American option = European option. > I think I might be confused by the fact that an > early exercise might not mean exercise and sell. Exercise DOES NOT mean to sell. Exercising means you exert your right to buy the underlying asset at the strike price, at your discretion. Hank Scorpio Wrote: ------------------------------------------------------- > Wouldn’t the minimum value for the American option > be the (underlying px - strike px) * risk free > rate ^ time to expiration? The min value American is min value of European which = underlying px - (strike px) / (1+risk free rate) ^ time to expiration
Thanks again for the replies. So for example, if I buy an american option in the market right now for company A. The strike price is say $20. The expiration is 3 yrs from now. Let’s say the stock price next year is $50. If this is an american option, I can exercise and sell next year and keep the $30. If this is a European option, I need to wait for 3 yrs and the stock price might be lower than $50 at that time. Therefore, an american option is > a european option. Is that assumption correct? Thanks.
Well, actually no. Assuming in this case, the stock does not pay any dividend, thus no underlying cash flow and a risk free rate of 10%. 1. American option will have same value as European option 2. The min value of American AND European option will be 50 - 20 /(1+10%)^3 = 34,97 Why is that? Because you can short the stock today to get 50 and invest in risk free. You position now is call + 50 - S. In three years, you will exercise your option --> buy the stock at strike price = 20 and settle your short. Your payoff will be 50* (1.1)^3-20 = 46,55 = FV(call option) = 34,97* 1.1^3. You can do this whether you own an American or European option. Why bother to exercise now when you can exercise in 3 years and get same benefit? So when the an American option is more worth than European option? It is when the stock gives out dividend. Say it gives a dividend of 12 every year. If you exercise now, you can get 12*3 = 36 USD (on a non discount basis) while if you wait 3 years (or you utilize the strategy above), you don’t get this cashflow. Hope it is clearer now.
Thanks for the clarification. It is definitely clearer now! So, based on your reasoning above, are we making the assumption that it does not cost anything to short the stock for the remaining years until the option expires?
correct. You assume that the 50 you got in an account earning risk free and the call are good enough collateral so it does not cost you anything
Contrary to what the CFA material says, even if a stock pays dividend, an American style option is worth at least as much as a European style option. For exam purposes, go with CFA material.