see this statement, the possibility of early exercise is not valuable for call option on non dividend paying stocks, so the value of european and american call are the same
ok, why is this statment correct, say you call because your bond is getting too expensive, right? or I missed something here you call because you are paying too much dividend?
Before someone can explain this more intuitively, consider it from the put-call parity (bear with me for a minute):
c+K/(1+r) = p+S
c=p+S-K/(1+r)
If we drop p from the equation, we can arrive at the following relationship (since p is always positive)
c>S-K/(1+r)
If we also assume r>0 (which is almost always the case) then we arrive at this relationship
c>S-K or call value is greater than the exercise value!
That means it is always better to sell the call than to exercise early. Since you can sell call in any case (whether American or European) that means American has no advantage at all
Fixed that for you.
Your conclusion’s still true, but it’s probably easier to arrive at it by starting with:
time value > 0
OK thanks. I also think the expression must be c>(S0-pv of K) to make it fully transparent, but it would become messy.
i might be really stupid but can you go into details about this?
If you exercise an option early, the only value you receive is the intrinsic value.
If you sell an option, you receive both the intrinsic value and the time value.
If the time value is positive and you want to get rid of the option, you want to sell it, not exercise it.
In short, there are only very rare occasions when you want to exercise an American option early. And if you’re not going to exercise it early, it isn’t worth any more than one which you cannot exercise early: a European option.
Another reason is that Buying a call is like buying insurance on the stock underperforming at expiration. If the option goes ITM, you might exercise it (american option) but this is why it’s unfeasible: option price paid at initiation is 3, strike is 50 & stock price today is 55, you’ll get a 5-3=2 profit(plus $2@rf rate). At/before expiration if the stock is at/below 50 odd then you’re ending up holding a poor stock coz you’ll be selling the stock for a loss nor will you have been able to sell the Option to close at a profit. If you didn’t exercise the option, you’d have let it expire worthless and could’ve bought the stock lower. If it had dividends, you might have exercised it before the ex dividend date since the benefit of the dividend doesn’t accrue if you hold the option.