An upper bound for call options

CFA Level I
#1

At Reading 63, top of page 103 there is a sentece saying:

“A call is a means of buying the underlying. It would not make sense to pay more for the right to buy the underlying than the value of the underlying itself.”

I am having a hard time conceptualizing this one. Granted we are talking about theoretical upper bounds and not realistic senarios, why should there even be an upper bound based on the quote above? I find two issues with this reasoning :

  1. A call, as I see it, is not a “means of buying the underlying” but “a means of buying the future underlying” which is by itself a different underlying. (it has an unknown value with a domain of [0, +inf) )

  2. Why does it not make sense to pay more for the right to buy it than the current value of the underlying - at least in theory? Let’s say that a trader has good reasons to believe that an asset will rise x times its current value within a time period. Why wouldn’t he pay an inflated price to get hold of a buying right? Even if the right itself is more expensive than the exercise price, as long as the expected value of (Future Value) - Exercise price - Call Price > 0

I simply cannot see how the quoted sentence (by itself) contains enough evidence for this upper bound.

Sorry for the English, I hope this is clear!

#2

Because you can realize that future value by buying the underlying directly. Example:

A stock ABC is trading at $100/share. You believe that in 6 months, it will easily go to $300. A call with exercise price of $5 (really low exercise price) is selling for $125.

If you buy the call and exercise it, you will pay $130/share.

If you just buy the underlying now, you will pay $100/share.

There is no scenario in which it makes sense to buy a call priced at more than the current price.

#3

Perfect. Thank you so much, your got me out of the mindblock :slight_smile: