Options – Is Time Relative?

I have been writing recently (see articles here and here) about the factors that influence option prices. Specifically, I’ve been talking about the things that affect the time value portion of an option’s price. Last time I described the effects of changes in “implied volatility,” which is another term for crowd expectations.

Another major factor in the amount of time value in an option is the amount of time remaining until that option expires. The more time there is, the farther the stock could move in that time; and the farther into the money the option could get. So options with a lot of time remaining have a lot of time value, while those with little time remaining have less time value.

Every option that today has very little time remaining, once had much more time remaining, and therefore more time value, than it has now. So it must be true that options lose time value as time passes. In fact they do, and at a predictable rate. That rate is not the same every day. It starts out very slow and accelerates as time passes. To understand why it must accelerate, think about this.

At expiration, the underlying stock’s price will be at one and only one amount. All of the options that are in the money at that time (calls with strike prices below the closing price, and puts with strike prices above it) will have value. All others will be worthless. Every option that is in the money at that time has a 100% chance of finishing in the money. Every other option will have a 0% chance. Those are the only possibilities: 100% or zero percent.

Right up until the moment of expiration, though, it wasn’t a 100% vs 0% situation. As long as there was any time remaining during which the stock could move, the question as to whether any option would finish in the money was not absolutely certain. The movement that could happen in the remaining time could still be decisive.

But the closer the time gets to expiration, the smaller the amount of movement that is likely during that time. If a stock has moved an average of $1 a day over the past 30 days, the chances of its moving $5 today are pretty small. So if a given option would require that $5 move to get into the money, its time value will be very small.

Let’s say that option, that is now about to expire, began life a year ago, and that the stock was the same price then as it is now ($5 away from the strike). Then, the chances of the stock moving $5 before expiration were much better – it had a year to do it. The time was very valuable, because the movement that could happen in that time (a whole year) had a good chance of eventually placing the option in the money.

With every passing day, the chance of that $5 movement decreases. At first, the difference is very small. From day 365 to day 364, the difference in the probability of that $5 move barely changes, so the time value does the same. Several months later, the passing of a day will be a bigger deal. When there are 10 days to go for example, losing the next day will have a big impact on the chances of that $5 move. We will have drawn one day closer to that moment when the probability will become zero. The difference between the chances on day 10 and day 9 are huge, where the difference between the chances on day 365 and 364 are trivial. So much more time value is lost with 10 days to go. Which was more than was lost with 11 days to go, and so on.

The rate of loss of value due to time decay can be estimated quite precisely by the option pricing formula. It is one of the Greeks, or variables that describe option price changes. It is called Theta. On our option chain, Theta is shown for every option. A Theta reading of .11 means that the option price will drop by eleven cents per share ($11.00 per contract) in the next day due to the passage of time. This is separate from any change that will occur due to the stock price moving. It is also separate from any option price change due to changes in crowd expectations about the stock (implied volatility).

In the last two weeks, we’ve discussed the effects on time value of crowd expectation, and of the time remaining until expiration. These are basic concepts that we build on in our option trading classes. They form part of the foundation that, with proper education, can help you to become a successful option trader.

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