A call option gives the holder the right (not the obligation) to buy a specified quantity of the underlying at a specified strike price by a specified expiration date.

For Example:
An issuer sells a call option granting the holder the right to buy 100 shares of a certain stock at £10 each by a specified expiration date. If, on the expiration date, the stock were trading at £5, the holder would decide not to exercise the option, since they would be buying a stock worth £5 for £10, effectively losing £5 for each stock bought. The call option is useless and the holder loses the premium paid to the issuer for the option.

If, on the other hand, the stock were trading at £15 on the expiration date, the holder would exercise his option, buying total shares worth £1500 for only £1000.

A graph of profit / loss against value of stock at expiration:

                       |                 |      /
                       |                 |     /
                       |                 |    /
              profit   |                 |   /
                /    0 |_________________|__/_____________
               loss    |                 | /                 } option
                       |_________________|/                  } premiun
                       |                 |
                       |                 |
                           value of stock at expiration
Obviously the holder wants the stock to be worth more at the expiration date than the strike price, set when the option is bought.

A European call option can only be exercised at the expiration date, whereas an American call option can be exercised at any point before the expiration date.

I've used £s throughout as I am British, don't you know. Obviously, everything works just as happily with $s. Or ¥ or €s for that matter...
Yes, this write-up is pretty much identical to my put option write-up, but they are strongly related ideas...

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