Stratégies Options - Long Call Spread : Delta

We had seen that the call spread was the combination of two calls of the same term and with different strikes on the same asset, one which is bought and the other which is sold.

There are situations which seem optimal for buying a call spread, rather than any other strategy. To identify these situations, it is advisable to seize well the variations of the price of a call spread according to the levels of the underlying, the acceleration of value as well as its sensibility with respect to a variation of implied volatility.
The first one : the delta ∆.

I - The delta of a call spread

We shall suppose in what follows that we are a buyer of the call spread, the reasoning for the seller being the opposite.

The long call spread is the combination of a long call having a strike lower than the one that is sold.
When realized, this strategy is worth nothing more if underlying is under the strike of the long call, and is worth a fixed amount equal the difference between strikes for an underlying above the strike of short call. Between strikes, an amount costs equal in the difference between the level of the underlying and the long strike. Gains are limited as well as losses.

Intuitively, it means that under the long strike, the call spread is dominated by this call. The delta of the call spread must thus be similar (with some differences) to the behavior of that long call. As underlying goes up, the short call sets of the importance until equal the long call: the total delta falls then, until zero.

For our example, we choose the call spread 100/120, maturity 1 year, on an asset paying no dividend and interest rate are set to 5 %.
Volatilities for both calls are set to 30 %. We shall have the opportunity to see soon what it happens with different volatilities, in particular in the presence of skew.

II - The call spread delta graph :

Graphically we have :

According to the intuition, the delta is symmetric and strictly positive for this long call spread. Delta is increasing with respect to the spot and reaches a maximum between both strikes, then decreases until becoming zero.

It is worth to note that the delta is almost useless for an important maturity of the call spread no matter the strikes are away from each other, delta of the long call and that of short call being almost equal. The shorter the maturity, the more the call spread reacts to the variations of the underlying.

Next : Long Call Spread : Gamma
Previous : Long Put Spread : A First Attempt

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

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