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I understand it is never optimal to exercise an American call option early. [1] [2] However, here are my two contradictory thoughts about selling an American call option early.

Assumptions

  1. I can only buy or sell a call option, never exercise it.
  2. I am continuously bullish on the underlying stock.

Contradictory thoughts

  1. The probability of touching is twice the probability of expiring in the money. [3] This implies that the call option is twice as likely to meet a profit target prior to expiration than at expiration. Thus, it is more profitable to sell early.
  2. On the other hand, because I am continuously bullish on the underlying stock, it would make sense to wait for the stock to appreciate. Thus, it is more profitable to sell the call at the last minute.

Thus, is it ever optimal to sell an American call option early?

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1 Answer 1

up vote 1 down vote accepted

If the option is fairly priced, as under the Black-Scholes Model, one cannot gain by selling it early, because the money you get just reflects the fairly expected value.

If you think you have some inside-information to be bullish on the underlying, you would not sell it early, but this is then just your assumption, so as you may aswell assume to be bearish.

The notion that the probability of touching is twice the probability to expire in the money, does not take into account the actual (expected) payoff received: The call provides unlimited upside potential until maturity.

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