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Option Greeks

Delta Adds Up

In this section, we will learn an interesting characteristic of Delta is that it can be added up. We have already learnt that the Delta of a futures contract is 1. Now assume that I hold an ATM call option which has a Delta of 0.5. This in other words means that I am holding a half futures contract. Given this, if I hold 2 ATM options then it is as good as holding one future contract because 2 options of Delta 0.5 add up to 1.

 

Case 1. Nifty spot at 16000, trader has 3 different call options. 


 

The positive sign in the position column indicates a long/ buy position of call, hence positive Delta. So, the total Delta of the portfolio will be (0.8+ 0.5 + 0.3) = ₹1.6

 

This means that if Nifty moves up by 1 point, the trader will gain ₹1.6 and if Nifty moves down by 1 point, he will suffer a loss of ₹1.6. 

 

So, if nifty moves up by 50 points, the combined position is expected to move by (50*1.6) = ₹80 

 

Case 2.Nifty spot at 16000, trader holds a combination of call and put options. 


 

The Put option shows a positive position, which means it has been bought or the trader is long on that option. However, Put option has a negative Delta, hence (+1 * -0.9) = -0.9 .The Delta of the put position is negative.

 

Therefore, the combined Delta of the portfolio is (0.8 + 0.5 + 0.3 + 9- 0.9) = 0.7

 

This implies that if Nifty moves by 1 point, the total combined position will have an effect of 0.7 points. So, if Nifty moves up by 50 points, the profit (because positive Delta means gaining with price increase) will be 50*0.7 = ₹35

 

An important point to keep in mind is, Deltas of call and put can be added as long as they belong to the same underlying.

 

Let us consider one more example to explain the Delta:

 

Case 3 Nifty is at 16000


 

When the trader is selling a put, he is getting a positive Delta (because we know negative quantity into negative delta gives positive delta result). So the combined Delta of this portfolio is 0.8 + 0.5+ 0.3 + (-1.8) + 0.2 = 0

 

This creates a Delta neutral portfolio for him as the combined Delta is zero. So this portfolio has no impact with the spot price movement. However, Delta keeps on changing because of time and volatility, so a portfolio can be Delta neutral only for a moment. We will learn more about Delta hedging and Delta neutral in upcoming chapters.

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