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:
<html>
	<div id="jxgbox2" class="jxgbox" style="height:300px; width:400px;"></div>
</html>

<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:
<html>
	<div id="jxgbox" class="jxgbox" style="height:300px; width:400px;"></div>
</html>

<script>
  var board = JXG.JSXGraph.initBoard('jxgbox', {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 writecallpriceslider = board.create('slider', [[0,0],[0,300], [0.0,100, 300]], {name:'callprice write'}, {withLabel: false});

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

  var writecalloptionarrow1 = board.create('arrow', [[function(){return 0}, function(){return writecallpriceslider.Y()}],[function(){return strikepriceslider.X()},function (){return writecallpriceslider.Y()}]],{'strokeColor':'blue'});
  var writecalloptionarrow2 = board.create('arrow', [[function(){return strikepriceslider.X()}, function(){return writecallpriceslider.Y()}],[function(){return  strikepriceslider.X()+200},function (){return writecallpriceslider.Y()-200}]],{'strokeColor':'blue'});

</script>

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]]
bag
finance_public
created
Sat, 14 Jan 2012 15:05:32 GMT
creator
dirkjan
modified
Sat, 14 Jan 2012 15:05:32 GMT
modifier
dirkjan
creator
dirkjan