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I was reading a textbook and came across some surprising stuff in the section about gap options.

Let $X$ be a payoff function such that $X=\Big\{\matrix{0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ , \ \ \ \ S(T)\leq K_2 \cr S(T)-K_1\ \ \ \ ,\ \ \ \ \ S(T)> K_2}$

The payoff would be negative if $K_2<S(T)< K_1$. The textbook says:

Notice that sometimes the option holder is forced to exercise at a loss! Perhaps the name "option" is a misnomer.

This seems surprising. Is it true that gap options can incur loss for the option holder beyond the initial price? Can you be "forced" to exercise options?

I looked online and didn't find anything. Also, feel free to edit/migrate if necessary.

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  • $\begingroup$ So trigger is $K_2$ and strike price is $K_1$. Suppose $S(0) = 100$, $K_1 = 1000$ and $K_2 = 0$. For a Gap call option, as long as $S(t) < 1000$, you will certainly lose money on the option. So the option price should be negative. $\endgroup$ – nathanesau Jul 5 '15 at 22:32
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    $\begingroup$ @Joseph Malle Which textbook? $\endgroup$ – user16651 Jul 5 '15 at 22:55
  • $\begingroup$ @BehrouzMaleki Actex's book for exam MFE by Johnny Li $\endgroup$ – sudo rm -rf slash Jul 6 '15 at 0:29
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Trigger contracts certainly exist and sometimes the trigger is out of the money and so yes the holder loses out. I have seen traded swaps that cancel when a reference rate is passed and the cancelling is disadvantageous.

Stop thinking of the contracts as "options" and start thinking of them as derivatives.

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  • $\begingroup$ Do gap options usually have trigger contracts as described in the question? $\endgroup$ – sudo rm -rf slash Jul 6 '15 at 0:31

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