Stratégies Options - The Call Spread : A First Attempt

The call spread is a simple strategy which combines the purchase and the sale of two options of the same type, calls, on the same underlying, having the same maturity, with different strikes.

I - The Situation

When we buy a single call, we have a bullish view on the underlying. Plainly it means that we’re waiting for an increase, an up move on the asset.
A trader can perfectly have a bullish perspective on an asset, but a limited one. That is, he can very well anticipate an increase of the underlying, with a maximum target. It is then useless and even expensive to buy a single call.

II - How to use them

From the previous report, we can perfectly imagine that the operator wishes to be a buyer at the level K until a certain level K ' beyond which he certainly will give up the position. He wishes for example to buy an share from 100 euro but right now wishes to give up the increase beyond 120 euro, little convinced that the asset will rise beyond.

To be buyer from a level K can be translated by the purchase of a call struck at K, be a seller from a level K ' beyond can be translated by writing a call struck at K '.
In the example this above, the trader can buy a call spread 100/120 on this asset, he buys 100 call, and sells the 120 call.

III - Advantage

The major interest is that by buying a call struck at K and by selling the other one struck at K', the amount to be paid out is lower than the naked purchase, and in the eventuality the underlying does not exceed the level K ', the gains are identical to those that would have be accomplished by the purchase of a naked call struck at K.

a - Maximum gains are limited
The maximum gains are the difference between strikes, less net premiums.
If the call 100 was bought for $14 and the call 120 was sold for $7, the maximum gains are: 120-100 - (14-7) =20-7=$13 for each call spread.

b - The risk
The risk of the call spread is limited to the net amount paid out for the purchase of the call with strike K minus the amount collected by the sale of the call with strike K'.

By taking back the example this above, the maximum risk is 14-7=$7 . We can lose no more than $7 with this call spread (much less than $14 with the call 100 only!).

IV - Graphic Representations

This is a representation of a 1 year call spread 100/120 , with a 30 % implied volatility, and with an interest rate of 1 %. No dividends.

2D graph :

Break even is at : 100 + 7 = $ 107

3D graph :

Next : Long Put Spread : A First Attempt
Previous : Writing Calls

Download the pricer here

BASIC OPTIONS STRATEGIES - INDEX
BASIC OPTIONS STRATEGIES - CHAPTER I
BASIC OPTIONS STRATEGIES - CHAPTER II
BASIC OPTIONS STRATEGIES - CHAPTER III
BASIC OPTIONS STRATEGIES - CHAPTER IV

Tryphon Duranton