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I have seen the rationale behind why it is never optimal to exercise an American call option early, but have a question about it.

If the option strike price is $E=\$20$ and it expires at $T=1yr$, if the share price is $S=\$25$ at expiry, the profit will be $\$5$ per share. However, what if at $T=0.5yr$ the share price was $S=\$40$ following a jump in the price. Exercising at this point would yield a profit of $\$20$ per share.

Would it not be more optimal to exercise early, in this case?

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4 Answers

up vote 0 down vote

To put it simply, you will make more money by selling the option than by exercising it.

Because:

An option is worth its intrinsic value plus its time value.

The intrinsic value is how much you will make by exercising the option right now.

The time value is the price associated to hedging that the option gives you until it expires.

So, when you exercise the option, you only gain its intrinsic value, whereas if you sell if, you will gain the intrinsic value plus the time value.

To take an example,

If your strike is \$20 and that the share is worth \$25, exercising the call will give you \$5. But selling the call will give you \$5 plus the time value ($0.20 for example).

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If you can dynamically hedge then you can monetize the value of your option without prematurely exercising it. Before writing about Randomness and Black Swans, Taleb wrote a book on the topic. The short version of the story is find the DV01 of your position, and take an opposite position with the same DV01. (& if you want, line up the rest of the greeks)

If you can't dynamically hedge for whatever reason, then the "Don't exercise early" rule is not so black and white. For example, executives have shorting restrictions on their companies. In these cases, they may be restricted to exercising options early rather than dynamically hedging.

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Because if you sell, you will get a higher value than 20USD per share. You can think of the reason behind this added value is that having a deep ITM option is better than having a stock: your downside is limited. Therefore your option worth more on the market than it's exercise value. This is why you are better of by selling it in your case (if you know that the price will drop to 25USD).

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up vote 1 down vote

If you think the stock is going to continue going up, just wait. If you think the stock has reached its peak, then short it in the open market. If the shorted stock continues to climb, you can always cover with your call option. If however the stock falls below your strike price, then let the option expire and cover at the market price.

It's this very ability to choose the buying price (strike vs market) when covering a short sale that makes the option valuable. But of course, you can do the same thing with a European option! That's why the American option gives you no added value over the European option. There is no benefit to exercising an American call option early.

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But my example describes a profit that wouldn't be possible if the option was European, why isn't that a benefit? – dplanet May 13 '12 at 19:31
What are you talking about?! If you exercise now, you pay \$20 and sell at \$40. But the only reason to exercise now is if you believe \$40 is the highest the stock will get. It's foolish to exercise now if you believe the stock will go higher. If you believe the stock will max-out at \$40, then short it now and wait until the expiration to see what the market price is before buying it back. The market price could be lower than the exercise price, which is why you'd be giving-up money to exercise now if you believe it's going to fall further. – chrisaycock♦ May 13 '12 at 19:35
Okay, so say that the stock is going to go down to $15, lower than the exercise price - the option will be worthless, I'll make a loss. But had I exercised when the stock price was higher than the exercise price (not necessarily highest) I'd have made a profit. Isn't that more optimal than the loss that has been made by holding onto the option until expiry? – dplanet May 13 '12 at 19:38
Do you know what short selling is? I've mentioned it twice because it's the classic textbook argument against early exercise. If the stock is at \$40 now and you believe it will drop to \$15 by expiration, short the stock now, let your option expire, and then buy back the stock ("cover your short" in industry jargon) on the regular market. – chrisaycock♦ May 13 '12 at 19:40
Great, thanks. The rationale I read only gave the reason that you'll lose interest on the cash you spend to exercise the call option. – dplanet May 13 '12 at 19:45
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