Option early exercising

[anujanand]

Hello,

I have one quick question :- Why it is *never* optimal to exercise American call option early?

if market is upward trending and if profit is large enough why not exercise now and take profit? (i.e. what if market trend downwards etc?)

C >= c >= max {(S0 - X*Exp-rt), 0}

Similar argument has been given for Put options to make case for early exercise...

I am sure I am missing some thing obvious here :-(

In the slide is says (from mathematical standpoint..? - why is that?)

Thanks
A

 

[cash king]

The argument seems to be based on the concept that a call option's value (intrinsic value+time value) is always greater than its intrinsic value (St-X). In other words, since c>=St-X at anytime t before expiration, excercising the option early to lock in the intrisinc value is less attractive than selling the option to other investors to lock in the option value.

But what if the option is illiquid so we can't find someone willing to buy it at price near its theoretical value? John Hull provides an alternative mechanism that precludes early excercise of calls: you can choose to keep the option and short the stock to lock in a better profit than early excercising (it's simple to illustrate it).

But I sitll wonder if early excercising is possible in practice. When short-selling is forbidden, early excercising call options is still worth consideration when option becomes deep in-the-money.

What is the reality in practice?