# Time Value of Options

## Two options with different time to expiration

Consider two options with the following characteristics:

• Both options are American
• Both options are calls
• The underlying of both options is Microsoft stock
• The strike price of both options is 40

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.

Question: Which one of the two options would you prefer to own?

## Expectations of a call option owner

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?

## Two ways of making money from call options

How can you make money when you own a call option? You have two possibilities:

Possibility 1: 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 40.

Possibility 2: 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.

## You need the stock to go up quickly

Under possibility 1 you need the stock to move up from 30 to 40 before the option expires.

Under possibility 2 you need other people to believe it will happen.

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. If Microsoft gets to 50 or even 100 after a year, that won’t help you, as your option would not be valid any more.

You want the stock to go up quickly, before the option expires. In case of our two Microsoft options, you need a move from 30 to 40, or more than 30%. What do you think is more likely? Is it more likely that Microsoft goes up 30% during the next 1 month or during the next 6 months (which of course includes the next 1 month too)? The answer is obvious.

## For option owners, longer is better

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.

## Time value of options

This is called time value of options. Besides intrinsic value, time value is the second component of an option’s total value (and market price). In general, the longer time until expiration an option has, the higher its time value. You can look at time value as the price for the possibility that the option’s intrinsic value will increase until expiration.

## European options are slightly different

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. Most frequently traded options on stocks and ETFs are American options.

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