# How Does an Option Get Its Value?

## Time and Volatility Affect Option Values

When you own an asset, it is easy to understand that you earn money as the value of the asset increases, and that money is lost when the value of an asset decreases. It is more complicated to understand how money is made or lost when the investor owns a derivative product, such as an option.

A derivative is an instrument whose value is primarily dependent on the value of a specific asset (such as a stock or futures contract).

However additional factors often play a vital role in the value of that derivative, making it difficult for a novice investor to grasp how owning a derivative translates into a profit or loss.

### Background on the Value of Options

The value of an option depends on seven factors.

• The price of the underlying asset
• The option type (call or put)
• The option's strike price
• The number of calendar days remaining — before the option expires
• The dividend, if any
• Interest rates
• The volatility of the underlying stock

The final factor that determines the value of your option is volatility. Specifically, an estimate of how volatile the underlying asset will be between the current time (i.e., when you buy the option) and the time that it expires. Obviously, the future is unknown and the best we can do is to estimate the future volatility.

Because the past is always known, you can calculate the 'historical volatility' for a given asset over any number of trading days.

And this historical volatility is usually a reasonable estimate for future volatility — unless there is a specific reason for believing that the future volatility will not resemble its average. One such reason is that there is a known news event that is likely to have a significant effect on the price of the asset.

Such events are typically the release of the company's quarterly earnings, or news concerning the results of an FDA trial for a proposed new drug, etc.

### Example of a Call Option Value

Let's say that you own a 63-day call option, with a strike price of \$70 per share, on a specific stock, ABCD. The stock is currently trading at (i.e., the last trade occurred at) \$67.50. This stock pays no dividend. The prevailing interest rate is 0.30% per year. Each of these factors affect the value of the option and are known to everyone.

For ABCD, the estimated volatility is 23. Most brokers provide reasonable estimates for volatility for all stocks and indexes. Those estimates are based on the actual option prices and use something referred to as implied volatility (IV). Basically, IV is calculated by assuming that the current option price represents its true theoretical value. For now, there is no reason to delve into complex matters, such as understanding IV because there will be adequate time to do that as you continue to learn about options.

If you decide that it is worthwhile to own one (or more) of the call options described above, it is important to understand how the option gains or loses value over its lifetime.

"Lifetime" ends when you sell the option or when expiration day arrives.

Because our example uses a call option, you know that the option is worth more as the price of the underlying asset (ABCD) increases. The options world is filled with novice traders who bought call or put options, watched the stock price change as they hoped it would, and were dismayed to see that the market value of the option declined. To understand how that is possible, you must have a clear picture of how an option is valued.

### Why Option Values Change

Each of the factors described below is in play at the same time. Some of these factors that affect the value of the option are additive, while others work in opposite directions.

Certain things never change, such as the strike price and option type (call or put). However, everything else is subject to change.

There is a way (the Greeks) to estimate how much the value of the option changes when various things change, such as the stock price. But that is not the whole story. As time passes, the value of all options decrease by a known amount (Theta). If the company announces a change in the dividend, that causes option values to undergo a modest change. Interest rates may change, but they play a tiny role in determining the value of any option — with the possible exception of very long-term options.

The one factor that causes grief newer option traders is how the volatility estimate can change suddenly. Not only change but change by a very significant amount. Vega describes how much the option value changes when IV changes by one point. For example, once a company announces an expected news item, there is no longer any reason to anticipate that the stock will undergo a significant price change before the option expires. Therefore, the estimated volatility tends to plunge once the news is announced. Options bought just before the news event become worth a whole lot less after the news. Of course, if the stock price moves significantly in the direction you anticipated (up for call buyers and down for put option owners), then you may earn a big profit, despite the large decline in implied volatility (reminder, that is the new estimated volatility).

An unexpected world event can result in a severe stock market decline (or rally). For example, once markets re-opened after the 9/11 attacks, implied volatility was much higher and all option owners were rewarded with extra profits. As the market decline continued to increase on Black Monday (October 1987), implied volatility surged, reaching levels never seen again. Even call options gained value (in a declining market!) because IV was so high.

### Options and the Inexperienced Trader

The problem for an inexperienced trader occurs when the stock price moves gradually higher, and the option price tanks. To some people, that is impossible. Novices tend to believe that the game is rigged and that the market makers were out to cheat them. Nothing can be further from the truth. In reality, the trader lost money because he/she paid far more than the option was worth (due to its high volatility). It is very important to understand the huge role that volatility, and especially implied volatility, play in the price of an option in the marketplace. Be wary when buying options.

Now, take a further look at the example. Let's assume that no news is pending. Assume that three weeks pass and ABCD rallies to \$64. If all else remains unchanged, the value of the option (CBOE calculator) changes from \$1.40 to \$1.57. If another three weeks pass, the option is worth only \$0.98.

Thus, if you expect to make money when owning options, it is important to understand that the time required for the stock price change to occur is crucial to your eventual gain or loss. Sure, if you have unrealistic expectations, and hope to see the stock price move to \$75, then the clock is unimportant (as long as the price is reached before the options expire). But for normal situations, where your prediction may not come true for a long time, it is important to have some idea of the timing of the anticipated price change. Buying too much time (i.e., owning an option with a later expiration date) is expensive and undesirable. However, not buying enough time (i.e., the option expires before the price change occurs) is even worse. Therefore timing is just as important in guessing the price change if you expect to make money when buying options.

Option values depend on far more than the price of the linked asset.