Why is it said that early exercise of a (call) option is not recommended and it is always better to sell the option instead?
Is it just to avoid assignment fees?
Of course, we assume that the option became in-the-money before expiry date.
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While early exercise is generally not advisable, because the time value inherent in the option premium is lost upon doing so, there are certain circumstances under which early exercise may be advantageous. For example, an investor may choose to exercise a call option that is deeply in-the-money (such an option will have negligible time value) just before the ex-dividend date of the underlying stock. This will enable the investor to capture the dividend paid by the underlying stock, which should more than offset the marginal time value lost due to early exercise.
So the question is how well do you see the time value factor here?
The crucial insight is that the alternative to early exercise of an American call is not necessarily to hold it to expiry, but to sell it. And selling it, at its value, is always better than exercising it.
Note that this holds only for options on assets that don't pay dividends.
Here's the proof, using Put-Call-Parity.
We know that at expiry T, we have (using a Call and a Put both struck at K):
C(T) - P(T) = S(T) - K
(if this is not clear to you, consider the case where S is less than, equal to, or greater than K at maturity, and go through each of them.)
If the stock S doesn't pay any dividends (and there is no cost of carry etc.), we can replicate both sides now at time 0; we just buy one call, sell one put (that gives us the left hand side), buy the stock, and borrow money so that at time T we have to repay K (that gives us the right hand side). That means that now, we only need to borrow df * K, where df is the discount factor, and is less than one (assuming the good old pre-2009 world where interest rates are positive). Thus:
C(0) - P(0) = S(0) - df * K.
C(0) = S(0) - df * K + P(0).
That's the value of the call, if we sell it (or hold it). However, if we exercise, we only get:
C_ex = S(0) - K
Now, we see that C(0) > C_ex, because we subtract less (df*K < K), and add P(0).
For a deep in the money, it almost makes no difference because the intrinsic value, the price of the option, is seldom far above the liquidation value, the price of the underlying less the strike price.
For an at the money, ceteris paribus, an early exercise would immediately cut the value of the option to
0; however, life is not so simple as JB King has shown.
Purely theoretically, for an at or near the money option, an early exercise will be an instantaneous cost because the value after exercise is less than the previously trading or implied option price.