Secrets of Option Greeks Delta in option trading strategies

Add up the Deltas

The Delta has an interesting ability – it can be summed up!

Let me explain – we will revisit the Futures contract. We know if there is a change of 1 point in the spot value of the underlying, then it means Futures changes by the same amount. 

For example, when Nifty Spot moves from 8340 to 8350, we see that Nifty Futures also shifts from 8347 to 8357 (with an existing value of 8347 when Nifty Spot was at 8340). Therefore, if we assign a delta value to this Futures, it would be 1 as every 1 point move in the underlying brings an equivalent change in the Futures.

Assuming I buy 1 ATM option with a delta of 0.5, it is equivalent to possessing a half futures contract. Consequently, with 2 such ATM contracts, the total delta is equal to possessing 1 futures contract. Thus, the deltas of two or more option contracts can be combined to determine the overall delta of the position.

We can use a few examples to gain more knowledge on this subject.

Case 1- The Nifty spot is currently at 8125 and a trader has 3 distinct Call options.

Observations –

1. A positive sign next to the number 1 in the Position Delta column indicates a long position.
2. The delta for the joint position is a positive one, that being +1.25, indicating both the underlying and combined positions will progress similarly.
3. For every 1-point shift in Nifty, the total position changes by 1.25 points.
4. If Nifty increases by 50 points, it is estimated that the total position will climb by an amount equal to 62.5 points, which is a 25 percent increase.

In case 2, with the Nifty spot at 8125, the trader has a mixed position consisting of both call and put options.

Observations –

1. The overall delta for the combined positions is +0.25; this indicates that the underlying and the entire position will move in the same direction.
2. The integration of Deep ITM PE has resulted in a decrease in the overall delta of the position, rendering the combined position less exposed to any changes in the market direction.
3. For every 1-point movement in Nifty, the combined position experiences a change of 0.25 points.
4. If Nifty shifts by 50 points, the cumulative position should increase/decrease by 12.5 points, which is equivalent to 0.25 times the magnitude of Nifty’s movement.
5. It is crucial to remember that the deltas of calls and puts can be combined, as long as they refer to the same underlying asset.

Case 3 – Nifty being at 8125, the trader has a combination of Call and Put options. He has 2 lots of Put options.

Observations –

1. The combined positions have a negative delta, indicating that the underlying and this option would move in opposite directions.
2. The inclusion of 2 Deep ITM PE has made the entire position delta-negative, meaning it is now inclined to follow market trends.
3. For every fluctuation in Nifty, the combined position is affected by a variance of 0.75 points.
4. If Nifty rises or falls by 50, then the position will shift by a corresponding  50 * (- 0.75) = -37.5 points.

In Case 4, when the Nifty spot is at 8125, the trader holds both Call options and Put options with the same strike price and underlying asset.

Observations –

1. The 8100 CE (ATM) option has a delta of +0.5, indicating a positive relationship with the underlying asset. 
2. On the other hand, the 8100 PE (ATM) option has a delta of -0.5, indicating a negative relationship with the underlying asset. 
3. When these options are combined, their overall delta becomes neutral, with a value of 0. 

1.   This means that any changes in the underlying asset will not have an impact on the combined position. For instance, if the Nifty experiences a 100-point movement, the options positions in this case will remain unchanged, resulting in a change of 0 points.
2. Positions like this, with a combined delta of 0, are commonly referred to as “Delta Neutral” positions.
3. Delta Neutral positions will not be affected by any alterations in the market trend. They are effectively shielded from movements in the market.
4. Delta neutral positions may be influenced by factors such as Volatility and Time; this issue will be addressed later.

In Case 5, the Nifty spot is at 8125, and the trader has sold a Call Option.

Observations –

1. The ‘-1’ in the Position Delta column signifies a ‘short’ position.
2. It is evident that a short call option results in a negative delta, indicating an inverse relationship between the option price and the underlying asset’s movement. This aligns with the understanding that an increase in the spot value would result in a loss for the call option seller.
3. Similarly, when you short a put option, the delta becomes positive. This implies that the option price and the underlying asset move in the same direction. Consequently, an increase in the spot value would result in a gain for the put option seller.
   1. -1 * (-0.5) = +0.5

Let’s consider a scenario where the trader has a long position of 5 lots of deep in-the-money (ITM) options. We know that the total delta of such a position would be +5 * +1 = +5. This means that for every 1 point change in the underlying asset, the combined position would change by 5 points in the same direction.

It’s important to note that the same effect can be achieved by shorting 5 deep ITM put options. In this case, the calculation would be -5 * -1 = +5. The -5 indicates 5 short positions, and -1 represents the delta of the deep ITM put options.

This case study should have given you insight into the process of summing up the deltas of individual positions to determine the total delta. This technique can be very helpful when managing multiple options simultaneously and determining their combined directional effect.

I strongly advise you to always consider the change in each position when evaluating your overall position, as this will give you an idea of the risk and leverage associated with it.

Here’s something to note: 

Delta of ATM option = 0.5

When you have 2 ATM options, the total delta of the position would be 1.

For every point movement of the underlying, the overall position changes by one due to the delta value being one. This demonstrates how similar an option is compared to a Futures contract. However, it is important to note that these two instruments should not be seen as equivalents. The Futures contract is only impacted by market direction whereas options can be affected by a variety of variables beyond just price direction.

If you want to explore the margin perspective, consider an options contract rather than a futures contract. Be aware of its implications first, and we’ll discuss this further later on.