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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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There's a lot of confusion and misunderstanding in the two answers and some of the comments, regarding lack of time premium in deep ITM options:

  • The primary case is that if the implied volatility is low, there will be minimal time premium in deep ITM options.

  • The secondary reason is that if there is a dividend coming up, option premiums adjust accordingly. Put premiums increase and call premiums decrease.

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If the stock price ends up below the strike price, you've lost the premium. But because, in your hypothetical, the strike price plus the premium is equal to the current stock price, that means that if the stock price at expiry is above the strike price, it's the same as if you had just bought the stock. That is, you can pay the premium, and then pay the strike price, and not pay any more than if you had just bought the stock at its original price.

What this means is that you are getting the full benefit of buying the stock at its current price (if the stock goes up $X, the profit from buying the option will be the full $X), but less of the downside (the most you can lose is the premium).

This means that if you buy one of these options and then short sell the stock, there are situations where you'll make money (if the stock craters, your short position will make you more money than the option loses) and no situation where you lose money. This is known as "arbitrage", and one of the principles of economics is that with an efficient marker, arbitrage cannot persist. If a situation you describe were to exist, traders would do the combination described above (short the stock, buy the option), which would drive down the cost of the stock and drive up the cost of the option, until (premium+strike price) is significantly larger than stock price.

There's been mention of there not being any time value, and you've expressed confusion because in your hypothetical there is time between the purchase and the expiry, but what they're getting at is this lack of difference between (strike+premium) versus current price.

For the reasons I've given above, in the real world the strike price of an option plus its premium is higher than the price of the underlying. The amount of this difference reflects the uncertainty in future stock prices. Since options are hedges against volatility, the more uncertainty there is, the more it costs to insure against that volatility. So more volatility generally means higher option premiums. Since a longer time horizon means more uncertainty, this difference of strike price + premium - stock price is known as the time value. Since this works out to zero in your hypothetical, people are saying that there is no time value, and remarking on how unrealistic this is.

Getting back to your original question, you're right. Just as there's arbitrage between either of the options and the stock, there's arbitrage in buying A and writing (selling) B. There's no situation where B is better than A. Since both have the same value for strike price + premium, that means that if the stock goes up, it doesn't actually matter which one you have. But as long as there is a chance of the stock going down, A is better than B. If the stock craters, then you'll want to let the option expire unexercised, losing just the premium. Since A has a smaller premium, its possible downside is smaller.

You also said that you've seen both options being offered, and are wondering why anyone would take B when A is available. That is indeed odd, and calls into question whether there's some further information that's missing.

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