What is an Option?

Option Terminology

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Profit and Loss Diagrams

Hedging

Now that you have a basic understanding of the mechanics of real calls and puts, we can continue with more terminology which will help to shape your overall understanding of options. Let’s start with two of the most important terms you’ll need to know, which are intrinsic value and time value.

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**Intrinsic Value and Time Value
**In the previous section, we found out that some options have an “immediate value” or “immediate benefit” at the time they are purchased while others do not. It’s time now to introduce some more terminology that will help you understand why.

We discovered that an option’s price must reflect any immediate value in holding it. For instance, we found that the July $35 call could give a trader an immediate benefit of $2.11 since the stock is trading for $37.11. If the stock is trading for $37.11 and you have a call that gives you the right to buy the stock for $35, you’re better off with the call by $37.11 - $35 = $2.11. That $2.11 worth of immediate benefit must be reflected in the price and we see that it is since that call is priced higher at $2.70.

In option lingo, we’d say that the $35 call has $2.11 worth of *intrinsic value*. While learning about options, it will really help if you learn to substitute the words "immediate benefit" or “immediate value” for intrinsic value. If the stock is trading for $37.11, we know the $35 call must be worth at least $2.11 in the open market. *In other words, all options must be worth at least their intrinsic value. *We’ll find out why this relationship must hold once we talk about option pricing in a later section.

If there is any value in the option over and above the intrinsic value, it is called *time value *or* time premium*. (Some texts will also refer to this as *extrinsic value*.) The time value is due to the fact that there is still time remaining on the option. Since the July $35 call was trading for $2.70 and the intrinsic value is $2.11 then the time value must be $2.70 - $2.11 = 59 cents.

Any option's price can be broken down into the two components of ** intrinsic values** and

Formula 1:

**Total Value (Premium) = Intrinsic Value + Time Value**

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Using the July $35 call example, we know that the intrinsic value is $2.11 and the time value is 59 cents so the total call value must be $2.11 intrinsic value + $0.59 time value = $2.70 total value. Figure 1 may help you to visualize the breakdown of time and intrinsic value:

Figure 1: Breakdown of TIME and INTRINSIC values:

If there is no intrinsic value then the option’s price is comprised totally of time value. For example, in Table 1, the July $37.50 call is trading for $1.05. However, the stock is only $37.11. If you buy the $37.50 call, you’re buying a coupon that gives you the right to buy the stock for a higher price than it is currently trading. On the surface, it may seem that the $37.50 call has no value. But the real way to say it is that it has no intrinsic value; the $37.50 call has no “immediate benefit” or “immediate value.”

Sure, there may be an immediate benefit in the future, but there’s no immediate value at this time. The $1.05 premium on this call is made up purely of time premium. The only reason value exists on this call is because time remains.

Using Formula 1 for the July $37.50 call, we have $0 intrinsic value and $1.05 time value so the total value is $0 intrinsic value + $1.05 time value = $1.05 total value.

If you like mathematical formulas, you can find the intrinsic value of a call by taking the stock price minus the strike price. If that number is positive, there is intrinsic value in that call option.

**Intrinsic Value Formula for Calls:**

Stock price - Exercise price = Intrinsic Value (assuming you get a positive number).

For example, the $35 call must have intrinsic value since $37.11 - $35 = $2.11. The $37.50 call, on the other hand has $37.11 - $37.50 = -39 cents. Since this number is negative, there is no intrinsic value for this call.

For puts, we use the same reasoning but in the opposite direction. In Table 1, the July $40 puts are trading for $3.20. There is obviously an immediate benefit in holding the $40 put since we could sell our stock for $40 rather than the market price of $37.11. The amount of that benefit is $40 - $37.11 = $2.89. The intrinsic value is therefore $2.89. Because the put is trading for $3.20, the remaining value must be time value. The time value is $3.20 - $2.89 = 31 cents.

Once again, using Formula 1 we see that the $2.89 intrinsic value + $0.31 time value = $3.20 total value.

If you wish to use mathematical formulas to find intrinsic value for puts, we can just reverse the call formula (remember, puts are like calls but they work in the opposite direction).

For put options, if the exercise price minus the stock price is positive then there is intrinsic value. For example, the July $40 put has intrinsic value since $40 exercise price - $37.11 stock price = $2.89 intrinsic value. We know this is the intrinsic value since the result is a positive number. The July $35 put, on the other hand, has no intrinsic value since $35 exercise price - $37.11 stock price = -$2.11 (negative number).

Intrinsic Value Formula for Puts:

**Exercise price – Stock Price = Intrinsic Value (assuming you get a positive number).**

We can rearrange Formula 1 to come up with another useful formula for finding time value. That is, Total Value – Intrinsic Value = Time Value. What is the time value for the July $35 call? The total value is $2.70 and the intrinsic value is $2.11 so the time value is $2.70 - $2.11 = 59 cents. The time value for calls and puts can always be found by Formula 2:

Formula 2:

**Total Value - Intrinsic Value = Time Value.**

Intrinsic value is the key value to solve for. If you can find intrinsic value, you can find time value. I can’t emphasize enough the importance of practicing by using the words “immediate benefit” or “immediate advantage” to determine if an option has intrinsic value. Formulas are nice if you are programming a computer but they do not allow you to understand why the formula works. Understanding why is important if you want to understand options. Use phrases such as “immediate benefit” to develop your understanding; use formulas to check your answers.

Let’s run through the thought process again for finding intrinsic value. For example, if someone asks you if the July $35 call in Table 1 has intrinsic value, you should ask yourself if there is an “immediate advantage” in being able to buy stock with the call for $35 when the stock is trading for $37.11. The answer is obviously yes. That means the $35 call has intrinsic value.

How much intrinsic value? We just need to figure out the size of that advantage. If the stock is $37.11 and you can buy it for $35, there is $37.11 - $35 = $2.11 worth of advantage in the $35 call. The intrinsic value must be $2.11. Any remaining value in the option’s price is due to time value. Because the option is trading for $2.70, there must be 59 cents worth of time value. Not too difficult, is it?

Let’s try working through the same question for the $40 put. Again, we know there is an “immediate advantage” in being able to sell your stock for $40 rather than the current price of $37.11 so this put has intrinsic value.

How much intrinsic value? Again, we just need to find out how big the advantage is. If the owner of that put can sell stock for $40 when the stock is trading for $37.11, there must be $40 - $37.11 = $2.89 worth of intrinsic value. Any remaining value in the option’s price is due to time value. Because the option is trading for $3.20, there must be $3.20 - $2.89 = 31 cents worth of time value. If you run through these steps every time you look at an option quote, intrinsic and time values will become second nature to you.

- In-the-money

- Out-of-the-money

- At-the-money

The phrase “in-the-money” is generally used to imply that something is profitable. If someone says their new business is in-the-money, it means they are making money and that’s really what this term is implying with options.

For example, in Table 1 (reproduced again below), the $32.50 and $35 calls are in-the-money since both have intrinsic value. The owners of these calls are able to buy the stock for less than it is currently trading and therefore represent an immediate benefit in holding the option.

**Table 1 (Reproduced)
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Technically speaking, an at-the-money option has a strike that exactly matches the price of the stock. In practice though, you’ll find that it’s pretty rare for the stock price to exactly match a particular strike. Because of this, we usually label the at-the-money strike as the one that is closest to the current stock price. In Table 1, we’d say that the $37.50 strikes are at-the-money calls (even though they are technically slightly out-of-the-money). These definitions apply regardless of the expiration month.

If an option is very much in-the-money (usually by a couple of strike prices or more) the option is considered *deep-in-the-money*. If it is several strikes out-of-the-money it is considered to be *deep-out-of-the-money*.

For put options, the same definitions apply; all strikes with intrinsic value are in-the-money. For puts, this means that all strikes higher than the stock’s price are in-the-money.

Let’s take a look at the puts in Table 1 below:

**Table 1 (Reproduced)**

The $40 puts are in-the-money since they have intrinsic value. The $32.50 and $35 puts are out-of-the-money since they have no intrinsic value. The at-the-money strike will be the same for calls and puts so the $37.50 puts would be considered the at-the-money strikes (even though they are technically slightly in-the-money).

The terms in-the-money, out-of-the-money, and at-the-money are sometimes referred to as the *moneyness* of an option.

These terms are used for description purposes; it just makes it easier for option traders to describe types of options and strategies. For example, rather than tell someone that you bought some call options whose strike price is lower than the current value of the stock, it's easier to say you bought some in-the-money calls. To get more specific, you may say you purchased some calls that were three dollars in-the-money.

If you purchased out-of-the-money calls and the underlying stock made a sudden, aggressive move, you may say your out-of-the-money options became in-the-money.

Table 2 describes the mathematical relationships for moneyness:

**Table 2
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Most option exchanges always provide at least one in-the-money and one out-of-the-money option for each expiration month. This means that as the stock moves to new highs (or lows) then new strikes will be added to each expiration month. So just because you see a certain number of strikes for a particular month today does not mean that list will remain the same size through expiration. New strikes may be added as the stock price moves to ensure there are in-the-money, at-the-money, and out-of-the-money calls and puts at all times.

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**Moneyness Affects Time Values
**The moneyness of an option affects the amount of time premium present. In general, in-the-money and out-of-the-money options will have the smallest time premiums. At-the-money options have the greatest amount of time premium.

For example, Table 3 shows the time values for the July calls and puts in Table 1. Notice that the at-the-money strike ($37.50) has the highest time values of $1.05 and $1.01 respectively:

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**Table 3
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Figure 2 below shows the intrinsic and time values for the same call options in Table 3. You can see that the time value (red) is very small for the $32.50 call because it is so far in-the-money. That strike is almost pure intrinsic value:

**Figure 2
**As we increase the strike price, the time premium gradually increases (the red portions get bigger) until we’re only left with pure time premium (solid red bar) such as the $37.50 strike. But as we move further out-of-the-money, the pure time value is again reduced.

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Another way to see Figure 2 is that the maximum red bar (time value) occurs for the $37.50 strike, which at-the-money. The red portions (time values) gradually decrease as you move away from that strike.

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An option that is trading for purely intrinsic value (i.e., no time value) is trading at

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**Wasting Assets
**We’ve learned that if you want a call or put option you must pay money for it. We also know that options expire at some time and that leads to an interesting question. Do options lose all of their value at expiration? After all, if the option is no longer good, how can it have any value?

While it is true that an option loses some of its value with each passing day, there is often a big misconception about how much of that premium is lost at expiration. There are traders who will tell you that *all* options become worthless at expiration and that is simply not true. In an earlier section we said that all options must be worth at least their intrinsic value – and expiration time is no different.

At expiration, all options lose only their *time value* but not their intrinsic value. It is only the time value portion of their price that slowly erodes with the passage of time, which is a process called *time decay*. The intrinsic value remains intact.

This is one of the reasons that it is so important to understand how to decompose an option into its intrinsic and time values. Certain strategies rely on the use of intrinsic values while others make use of the time values. If you want to trade, hedge, or invest with options, you need to know how much of each value is present at each strike price.

To make sure you understand this concept, let’s look at the August $35 call in Table 1, which is trading for $3.60. We know there is $37.11 - $35 = $2.11 worth of intrinsic value and that means that the remaining value, or $3.60 - $2.11 = $1.49 worth of time value. If you were to buy this call and eBay closed at the same price of $37.11 at expiration, the $35 call would still be worth the intrinsic value of $2.11. It would not be worth zero. The only amount you would lose is the $1.49 worth of time premium.

Remember, traders are paying the additional $1.49 over and above the immediate value because there is time remaining. Once time is gone (option is expired), then there can be no time value on the option but the intrinsic value will remain.

In Figure 2, the intrinsic and time values are colored green and red respectively. It is only the red portion that erodes with time. (Bear in mind this doesn’t mean that you cannot lose the intrinsic value. However, that value can only be lost due to adverse stock price movement and not the passage of time.)

Because options lose some value with each passing day, they are called *wasting assets*. There are some investors who reject the use of options since part of the option's price deteriorates simply by the passage of time but that is a shortsighted reason. The car you drive loses value over time. The same is true for the fruits and vegetables you buy. What about the computer you use?

It doesn't make sense to say that it's not worthwhile to invest in assets whose value depreciates over time. You just have to be careful in the way you use them. Nearly all assets deteriorate over time so don't back away from options just because a portion of their value depreciates over time. Even the expensive factories that General Motors, Dell Computer, or Intel has built all lose value with each passing day but the CEOs will tell you they have been very productive assets.

**More on Time Decay
**Time decay does not occur at a constant rate over time. In other words, an at-the-money option with 30 days to expiration does not lose 1/30 of its value each day. Instead, it is an accelerated loss and it loses progressively more and more each day. This is called

Figure 3 shows the price of a 90-day option priced around $5.50 and we assume that nothing changes except the passage of time. You can see the rapid deterioration of the time value as we get closer to expiration – especially in the last thirty days.

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**Figure 3
**Some texts will show this chart in the reverse order with the numbers on the horizontal axis increasing from 0 to 90, which is probably more mathematically correct since the numbers are ascending as we move left to right. However, it makes it awkward to read since you must make time move from right to left as we approach expiration. It’s usually easier for people to visualize time moving forward by moving from left to right.

It’s a matter of preference as to which type of chart you use. Just realize that as you continue reading about options that you may encounter time decay charts that appear backwards but it’s just due to two different styles of presenting the same concept. The important point is that you understand that time decay is not linear. Because of this, it is usually to your advantage to buy longer periods of time and sell shorter periods of time.