# Time Value of Out of the Money Options

## Time value of at the money vs. in the money options

In the last two articles we have explained why time value of at the money options is higher than time value of in the money options (it can be explained by the factors of risk and interest). We have not talked about out of the money options, so let’s look at them now.

## Zero intrinsic value

Out of the money options have zero intrinsic value and their market price is equal to their time value. In this sense they are the same as at the money options. You have no intrinsic value to pay for when you are buying an out of the money option and therefore your maximum risk of holding the option will be limited to its time value. Also the interest factor will be similar to at the money options – you pay less for the option, which means less interest or opportunity cost in terms of time value of money.

## Profit potential of out of the money options

On the risk side out of the money options are the same as at the money options and knowing just this, we might conclude that their time value should be much higher than time value of in the money options.

But there is the second factor in the equation, namely the profit potential. When you are buying an out of the money option, you are basically hoping that the underlying asset will move sharply and quickly in your direction. Let’s say you are buying an out of the money call option on Bank of America stock. The strike price is 40 dollars, while the stock is trading at 20. If you hold the option till expiration and hope to exercise it, you need the stock to go above 40 (it means to double) to get any intrinsic value.

At the same time, someone who is buying another Bank of America option with strike price of 20 needs the stock to climb just a few dollars above 20 (it’s current price) and he will get 1 dollar for every dollar above 20 at expiration. You see the profit potential is vastly different here.

How likely is that the owner of the 40 dollar strike call will get any cash at expiration? And how likely is it for the owner of the 20 dollar strike? If the two options were trading at the same price, which one would you prefer to buy? The lower strike of course.

## The further out of the money, the lower price

Market knows this too and that’s why options with same underlying, same expiration date, but significantly different strikes trade at different prices. The further out of the money an option is, the lower its market price. Because the market price of at the money and out of the money options is made up from time value only, we can conclude that time value of options declines the further out of the money they are (other parameters being equal). This is valid for both calls and puts.

## Arbitrage explanation

If it were not valid, there yould be a riskless profit opportunity in the market. If the Bank of America 20 and 40 strike calls with same expiration date traded both at 2 dollars let’s say, you could do the following:

1. buy the 20 strike call
2. sell the 40 strike call

It would cost you zero (not considering commissions and fees). What will be your result under different scenarios?

• If Bank of America stays at or under 20 by expiration of the options, you get nothing and both options are worthless. But you also don’t lose anything. Result is zero.
• If Bank of America ends up somewhere between 20 and 40 by expiration, your 20 strike call will be worth the stock price less 20 (your net cash inflow when you exercise the option and sell the stock immediately). The 40 strike call will be worthless. You’ve made a profit.
• If Bank of America stock shot up and ended up above 40 by expiration of the options, let’s say at 45, you would make 45 less 20 = 25 on the 20 strike call and lose 45 less 40 = 5 on the 40 strike short call (the owner of the 40 strike call will exercise it and his profit will be your loss). Your total net profit will be 25 less 5 = 20 dollars per share (equal to the difference between the strike prices).

Under any circumstances, you either make a profit or end up break-even. Anyone want a riskless free profit opportunity?

But such opportunities are extremely rare. In practice this could maybe happen on very close strikes (like 20 and 21) and it would only last for a few seconds before somebody (a person or more likely a computer) would discover it and profit from this opportunity, which would bring the prices back to where they normally should be – the further out of the money option cheaper than the option closer to the money.

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