The only difference between the two options is the expiration date. The first call option expires in one month and the second call option expires in 6 months. Microsoft stock is currently trading at 30 in the stock market, or 10 dollars below the strike price. For calls this means that the intrinsic value is zero at this moment.
What does someone who would buy or own any of these two call options think and expect? He expects Microsoft stock to go up quite significantly. If the stock stays somewhere around 30 or even goes down, the call option representing the right to buy it for 40 will not be very valuable. Why would anyone buy a stock for 40 when he can buy it somewhere else for 30?
You can exercise the option. If you want to exercise the call option, you need its intrinsic value to be positive. In our case, you need Microsoft stock to trade higher than You can sell the call option to someone else for a price which is higher than for what you have bought your option. If you want to sell the option for a higher price, you need the market participants to think that the prospects of exercising the option have improved, so they would be ready to pay more for the option.
It means that the market participants would have to think that the probability of Microsoft stock getting over 40 before the expiration of the option has increased. In any case, you want the stock to go up. But solely the stock going up is not enough, because there is a time pressure for you, as your option has limited life.
You want the stock to go up quickly, before the option expires. What do you think is more likely? The answer is obvious. Answer to the question: Owning the 6 month option is better than owning an otherwise identical 1 month American option.
The longer the time to expiration of your option, the longer you will have the right to choose if you exercise or not, and the higher is the probability that the market price of the underlying stock will move to a level at which it is favourable for you to exercise the option or to sell the option at a profit.
This is called time value of options. In general, the longer time until expiration an option has, the higher its time value. Note that we have been talking about American options, which can be exercised any time before expiration. European options are slightly different, as they can be exercised only at the moment of expiration and not before that.
European options have time value too, but in their case it is a little bit more complicated. So for now we stay with American options.
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Tutorial 1 Tutorial 2 Tutorial 3 Tutorial 4. Option Time Value Explained.