Are there any investment strategies which take advantage of an in-the-money option price that incorporates no "time value"?

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.

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 => 3.50Vol = 75 => 3.54Vol = 100 => 3.63Vol = 150 => 3.94Vol = 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.

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.