Call options

A call option is the 'right but not the obligation to acquire an asset by paying a certain sum of money on or before a certain time. A call option gives the buyer of the option the right to buy the underlying asset at a fixed price (strike price or K) at any time prior to the expiration date of the option. The buyer pays a price for this right.

At expiration,

• If the value of the underlying asset (S) > Strike Price(K)
  • -> Buyer makes the difference: S - K
• If the value of the underlying asset (S) < Strike Price (K)
  • -> Buyer does not exercise

More generally,

• The value of a call increases as the value of the underlying asset increases
• The value of a call decreases as the value of the underlying asset decreases

A Pay-off Diagram for the buyer of call option looks like this:

<script>

 var board = JXG.JSXGraph.initBoard('jxgbox2', {boundingbox: [-40,  150, 300, -150], keepaspectratio:true, axis:true});

 var strikepriceslider = board.create('slider', [[0,0],[300,0], [0.0,100, 300]], {name:'strikeprice'}, {withLabel: false});
 var callpriceslider = board.create('slider', [[0,0],[0,-300], [0.0,-100, -300]], {'strokeColor':'red'});

 var strikepriceline= board.create('line', [[function(){return strikepriceslider.X()}, function(){return -150}],[function(){return strikepriceslider.X()},function (){return 200}]],{'strokeColor':'red'},{'dash':'true'});

 var calloptionarrow1 = board.create('arrow', [[function(){return 0}, function(){return callpriceslider.Y()}],[function(){return strikepriceslider.X()},function (){return callpriceslider.Y()}]],{'strokeColor':'green'});
 var calloptionarrow2 = board.create('arrow', [[function(){return strikepriceslider.X()}, function(){return callpriceslider.Y()}],[function(){return strikepriceslider.X()+200},function (){return callpriceslider.Y() + 200}]],{'strokeColor':'green'});

</script>

A Pay-off Diagram for the seller of call option ('writing' a call) looks like this. In the interactive diagram below, the blue line represents the call option for the seller:

This diagram simply reflects that of the time of the purchase the buyer has a 'loss' (reflected by the purple arrow) and that the profit of a call option kicks in when the share price - the cost of the call option is bigger than zero.

There is a difference between European call options and American call options:

• European calls are only exercisable at expiration.
• An American call may be exercised at any time prior to expiration.

As a consequence, an American call must be at least as valuable as on otherwise identical European call. The distinction between American and European options is very important for Real Options. Real options typically can be exercised early and the value of the underlying asset is subject to erosion by competitors.

See also: Put options