Early exercise of american call (Market A - part 2)

[sathyat]

Hi David,
Why is it never optimal to early exercise an american call ?

Call is option to buy at a fixed strike price. If the price is significantly above the strike on any particular day before the expiry then you could exercise the option, and sell the stock in the open market and make profit - isn't it ?

Regards,
Sathya

 

[David Harper CFA FRM]

Hi Sathya,

This is a interesting question for me b/c I used to do work pricing executive stock options, and when we'd try to make this claim to clients ("it theoretically never optimal to early exercise an american call"), nobody would believe it. I learned quickly, especially to grizzled Board members, to keep quiet about *theoretical* option pricing...and, all empirical research on this matter related to employee/executive stock options (i.e., American options where actual money is on the line), totally agree with you. Nobody who holds Americans seems to act according to this theory. 95% + of actual exercises are 0 to 24 months after vest, when you think you are goodly in the money

But Hull gives the theory in Chapter 9. Please note this is for non-dividend paying stock (theoretically, we expect dividend paying stocks to DROP IN PRICE ex-dividend; another simplyfing theory not necessarily true).

the idea is that, given you expect the stock to continue to grow, and yet the strike price is fixed, you are better to defer the strike (K). For example, if today strike is $10 and stock is $12, but will grow to say $13. If you defer, you earn incremental interest on the $10 strike in the meantime. There is another way to look at this:

option value = intrinsic value + time value

Due to this, an immediate exercise which could instead be deferred, realizes only the intrinsic value but "leaves on the table" the time value (and so it is better to collect the time value by holding)

But again, that's the theory, the AIM, the test, etc...if the point were to debate, I would prefer your side due to the fact this assertion omits a few things, but namely, that as the holder you may have a view on the current intrinsic value

David