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Suppose a stock is trading for $50. Further, suppose there is some call option A, which has a strike price of $40 and a premium of $10. Furthermore, suppose there is another call option B, which has a strike price of $30 and a premium of $20.

Assuming a buyer thinks the stock the will go higher, which call option should he or she buy and why?

If I get it right, one should always buy the one with the smaller premium, since if the stock would go down, the losses would be less. Is this true? I have changed the numbers but I see this particular situation at a real market, and cannot understand why it exists.

  • Your example is unusual because there is no time value. If there are more than 1 trading days remaining, buy the cheaper one because it will gain time value more quickly when this temporary anomaly corrects itself. – TainToTain Jun 9 '16 at 18:01
  • There are about 60 days left still. Why there is no time value? – fav Jun 9 '16 at 18:02
  • If the stock is trading at $50, then a call with strike of $40 is not at-the-money. A call with a strike at $50 is at-the-money. Maybe you should edit to clarify. – user32479 Jun 9 '16 at 18:05
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    Maybe stating the comment by @TainToTain slightly differently to try to clarify - In your example, the market price does not reflect any time value, and that is unusual. Since there's time left, you would expect that it does have some (theoretical) time value, so you're either seeing a momentary imbalance or there's something else going on. The former is unlikely but potentially profitable. The latter should be a source of concern since it may indicate that the street knows something that's not going into your accounting. – user32479 Jun 9 '16 at 18:19
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    I don't actually intend to do anything. I just try to understand what is happening there. I asked this question to learn more :) – fav Jun 9 '16 at 18:43
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As other uses have pointed out, your example is unusual in that is does not include any time value or volatility value in the quoted premiums, the premiums you quote are only intrinsic values. For well in-the-money options, the intrinsic value will certainly be the vast majority of the premium, but not the sole component.

Having said that, the answer would clearly be that the buyer should buy the $40 call at a premium of $10. The reason is that the buyer will pay less for the option and therefore risk less money, or buy more options for the same amount of money. Since the buyer is assuming that the price will rise, the return that will be realised will be the same in gross terms, but higher in relative terms for the buyer of the $40 call.

For example, if the underlying price goes to $60, then the buyer of the $40 call would (potentially) double their money when the premium goes from $10 to $20, while the buyer of the $30 call would realise a (potential) 50% profit when the premium goes from $20 to $30.

Considering the situation beyond your scenario, things are more difficult if the bet goes wrong. If the underlying prices expires at under $40, then the buyer of the $40 call will be better off in gross terms but may be worse off in relative terms (if it expires above $30). If the underlying price expires between $40 and $50, then the buy of the $30 will be better off in relative term, having lost a smaller percentage of their money.

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Your scenario depicts 2 "in the money" options, not "at the money". The former is when the share price is higher than the option strike, the second is when share price is right at strike.

I agree this is a highly unlikely scenario, because everyone pricing options knows what everyone else in that stock is doing.

Much about an option has everything to do with the remaining time to expiration.

Depending on how much more the buyer believes the stock will go up before hitting the expiration date, that could make a big difference in which option they would buy.

I agree with the others that if you're seeing this as "real world" then there must be something going on behind the scenes that someone else knows and you don't.

I would tread with caution in such a situation and do my homework before making any move.

The other big factor that makes your question harder to answer more concisely is that you didn't tell us what the expiration dates on the options are. This makes a difference in how you evaluate them. We could probably be much more helpful to you if you could give us that information.

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