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# Buy call option – At the money / In the money / Out of the money

__Definitions __

Buy call option – a stock option is the right to buy a stock (but not the obligation) at a certain price for a limited period of time. The price at which the stock may be bought is called the *striking price*.

Three terms describe the relationship between the stock price and the options striking price: At the money / In the money / Out of the money

For example; stock XYZ trade at $100

At the money – the strike price of the option is $100

In the money - the strike price of the option is $90

Out of the money – the strike price of the option is $110

The strike price is one of the 6 factors that determine the price of the option.

Those factors are:

1. The price of the stock

2. The strike price of the option

3. The time until the option expires

4. The volatility of the stock also called “implied volatility”

5. The risk-free interest rate (usually the 90-day treasury bills)

6. The dividend rate of the stock.

The last two have less influence on the option price.

The option pricing has two elements, “time premium” and “intrinsic value”.

In this post, I’m not going to elaborate on those two. (But they are important to understand).

__The Delta__

The delta of an option is the amount by which the call option will increase or decrease in price if the stock moves by 1 point. The values of the delta are between zero to one, if the call option is in the money the delta is closer to 1 if the call option is out of the money the delta is closer to 0.

For example; if the stock option has a delta value of 0.8, this means that if the stock increases or decreases in price by $1 per share, the option price will rise or fall by $0.8.

The option pricing is based on a partial differential equation because of that the behavior of the option pricing is not linear, as we can see from the charts.

In the right chart, we see In the money option with a delta of 0.92, meaning the option price is behaving very similar to the stock price, we see that the lines are nearly flat.

In the left chart, we see the Out of the money option with a delta of 0.12, meaning the option price does not move like the stock price, for every $1 the stock will move the option price will move $0.12.

Also, note the difference between the profit lines, to make 3 points with In the money option the stock needs to move to above $190, but the Out of the money option needs only to move above $145.

This was the profit side, the losing side as you can see if the stock will remain at the same place the In the money options will break-even while the Out of the money options will expire worthless and will lose 1 point.

The options that were used (input):

Right chart: Option price -> $25.9, Stock price -> $115 , Strike price -> 90$ , Interest rate -> 0 , Days to expire -> 56 , Implied volatility -> 40.8%

Left chart: Option price -> $1.17, Stock price -> $115 , Strike price -> $140 , Interest rate -> 0 , Days to expire -> 56 , Implied volatility -> 40.8%

One option contract is the right to buy 100 shares so the cost for the options would be: $2590 and $117 respectively, not include commissions. For clarification: If you hold it to expiration and it is not worthless, that means you need to buy 100 shares at the strike price, $9000 in the right chart, $14,000 in the left chart. (not include what you already paid)