# Maximum value of American call?

I’m reviewing this stuff for the first time…ouch. The maximum value of American call is <= price of the underlying, that’s how it is defined. Sure, a stock trading at \$23, will not have a call valued at more \$23, but why isn’t it this: maximum value (American call) <= Max of zero or (price of the underlying - strike price)? 1) strike price =\$20, Price=\$23, then Call=\$3 2) strike price =\$20, Price=\$20, then Call=\$0 3) strike price =\$20, Price=\$10, then Call=\$0 Why do they say it is <= \$23? I know I’m missing something…

Dreary, an option will never cost more than the underlying asset , “why spend \$24 for a call if I can buy the stock for \$23?”

strangedays, yes, i understand that, but what is the value of the call? Of course it is less than \$23…it’s also less than \$23*2=\$46…it’s also less than \$23+\$10, etc. That’s obvious. Why isn’t it less than or equal to (Price minus strike price)?

Because (price - strike) is the payoff of the call, which cannot be related to the price (you pay it at the beginning). The relationship: The maximum value of American call is <= price of the underlying, must be held all time, if this is not the case an arbitrage can be constructed going long asset and shorting the call.

ok, got that, thanks. It is possible that strike price =\$20, Stock Price=\$23, but if this call will expire in 6 months, it will be worth more than \$3, but will never be worth more than \$23. I’m a bit rusty with options

In other words, it is true that: maximum value (American call) <= (price of the underlying - strike price), or zero AT EXPIRATION.

Dreary Wrote: ------------------------------------------------------- > ok, got that, thanks. > > It is possible that strike price =\$20, Stock > Price=\$23, but if this call will expire in 6 > months, it will be worth more than \$3, but will > never be worth more than \$23. I’m a bit rusty with > options of if the stock price is below the strike the call is out-of the money and the payoff zero meaning you will not exercise the option

But get this: It says that “if the underlying pays no dividends, then there is no reason to exercise early.” But: strike price =\$20, Stock Price=\$23, 1 month to maturity. Isn’t it a good reason to exercise now to lock in a \$3 gain? You could wait, but then the stock price may drop below \$23 at expiration, and you will not make \$3 profit?

Sell the call…

Ah, Joey…good point I guess that’s what I was thinking … to get out! by excerising then immediately selling, which is same as selling the call…not a good idea to start reading a big topic days before the exam!

It also said that: " if the underlying pays dividends, then it maybe worthwhile to exercise early.". Fine, but shouldn’t that premium be built into the call, Joey?

Dreary Wrote: ------------------------------------------------------- > But get this: > > It says that “if the underlying pays no dividends, > then there is no reason to exercise early.” > > But: > strike price =\$20, Stock Price=\$23, 1 month to > maturity. > > Isn’t it a good reason to exercise now to lock in > a \$3 gain? You could wait, but then the stock > price may drop below \$23 at expiration, and you > will not make \$3 profit? If you think to hold the asset for more than one month, it is better to keep the option and exercise it at maturity. The exercise price, is paid one month after respect to the case if you exercise the option immediately. That means you will earn interest on the price of the strike. In addition, as the asset does not pay dividends you dont lose any additional profit. Finally, you still have the probability that in one more month the asset price will go below 40, hence if you hold the option you will max lose the strike price.

Has anyone out there bought/tried the Institute exams for June 2008? I am contemplating buying and would like to hear from anyone who has taken these practice exams and if they would recommend and if they are any different from what we get from the likes of Schweser. I am desperate

Joey what do you think?

i’d say the maximum value of call is, call’s worth keep on increasing the farther below it’s strike price is from the current price; the lowest you can get your strike price (ie. the right to buy something is 0) so the maximum value of call is when the strike price is at 0. and the value at that point is the difference between current tradin price and 0. (price - 0)

you just described a put.

what?!?!? am i smoking here or something wrong with my thinking.

Let’s take an example. Security price 10 Case a: strike price 10, call worth = 0; cuz i can go into the market and buy the stock Case b: strike price 15; call worth = 0 (should be negative, but whatever, no one wants to own this call cuz i can go out to the market and buy it) case c: strike price: 5 call worth: 5 + (transaction cost to buy this call) Case d (maximum a call can be worth) strike price: 0 (ie. the right to buy something for 0 and be able to sell it at 10) call worth 10 + transaction cost to buy call. So max value of call = price but less than price cuz there will be some transaction costs.

" if the underlying pays dividends, then it maybe worthwhile to exercise early.". Shouldn’t a premium for the up coming dividend be built into the call? So, what’s the advantage of excercising? Comments?

pepp Wrote: ------------------------------------------------------- > Let’s take an example. > > Security price 10 > > Case a: > strike price 10, call worth = 0; cuz i can go into > the market and buy the stock > > Case b: > strike price 15; call worth = 0 (should be > negative, but whatever, no one wants to own this > call cuz i can go out to the market and buy it) > > case c: > strike price: 5 call worth: 5 + (transaction cost > to buy this call) > > Case d (maximum a call can be worth) > strike price: 0 (ie. the right to buy something > for 0 and be able to sell it at 10) call worth 10 > + transaction cost to buy call. > > So max value of call = price but less than price > cuz there will be some transaction costs. pepp -sorry man, but you got this all messed up. Case A: Strike = 10 Underlier = 10 This is an ATM option and is only worth 0 at expiration. Prior to expiration it might be very valuable as it gives you the possibility tobuy something at 10 that might go to 100 or 1 billion. Case B: Ditto except this is an OTM option which willbe less valuable than an ATM optionof the same tenor. Case C: worth = 5 + time value.