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I'm not sure if "time value" is the correct term, but if an option (still at least several months from expiry) is trading at the difference between its underlying stock's price and its strike price, are there any strategies that can take advantage of this fact? In theory, I would think there should be at least some "extra" value to the option based on its underlying stock's potential to increase in price.

For example, consider a stock trading at $7.50, with its January 2014 $4 call option trading at $3.50.

I understand that "trading at" is a vague term, and I may not be able to buy or sell the option easily because of large spreads, and there are commissions, etc. - but for the purposes of this question, assume that I can buy or sell the option for $3.50 after commissions at the same time that I can buy or sell the stock for $7.50 after commissions.

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Options can have a negligible time premium. For American1 calls the time premium is never negative. If it had a negative premium it would be profitable to exercise it immediately.

A deep in the money call has a delta of exactly one. That is, it's price movements completely mirror the price movements of the underlying stock. That means an option seller can buy stock and completely hedge his short option position.

The seller of the option may be in an position to buy with very little margin and take your money and invest it.

For example, consider a stock trading at $7.50, with its January 2014 $4 call option trading at $3.50.

For one option, representing 100 shares, a trader could take your 350 dollars and invest it, and only use a small portion of the money to buy the stock on margin. Market-makers can typically borrow money at very low interest rates.

If you have high borrowing costs, or are unable to buy on margin, then buying deep in the money calls can be a good strategy.

Long story short, option sellers are making money off selling these deep in the money calls even with almost zero time premium. So, in general, there's no way to make money by buying them.

1. An American call is a call that can be exercised at any time up to and including its expiration date.

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It depends on the volatility of the underlying stock. But for "normal" levels of volatility, the real value of that option is probably $3.50!

Rough estimates of the value of the option depending on volatility levels:

Vol = 50  => 3.50
Vol = 75  => 3.54
Vol = 100 => 3.63
Vol = 150 => 3.94
Vol = 200 => 4.32

Bottom line: unless this is a super volatile stock, it is trading at $3.50 for a reason.

More generally: it is extremely rare to find obvious arbitrage opportunities in the market.

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The term for the difference between an ITM option's strike price and the underlying stock's price is called the INTRINSIC VALUE.

In your example, with XYZ at $7.50, if the Jan 2014 $4 call is trading at $3.50 then its delta is 100. If you buy this call instead of the equity, it is called a 'Stock Replacement Strategy' and it enables you to participate in upside gains dollar for dollar with less than half the risk ($7.50 versus $3.50).

If you wanted to leverage the bet, you could buy two calls rather than buying 200 shares on 50% margin, avoiding margin borrowing.

If so inclined, you could sell an OTM call against this long Jan $4 call, creating a diagonal spread. Some call this the "Poor Man's Covered Call".

If bearish, you could short this call rather than short the stock though it's not a good idea since with no time premium, there's a higher probability that you will be assigned early.

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you asked for strategies which use deep in the money options:

  • dividend mispricing can use deep in the money options, basically its an arbitrage play on ex-dividend dates.

  • and any kind of spread can use deep in the money options, depending on how wide you want your spread to be

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