# Professional Trading through Option Theory

## 11.1 - Adding up the Deltas

This is an interesting feature of the Delta: The Deltas can be added up!

Let me clarify - let's go back to Futures contract for a second. For every 1 point change in the spot value of the underlying, the futures will also change. If the Nifty Spot moves between 8340 and 8350, then the Nifty futures will also change from 8347 to 8357) (i.e. Assume Nifty Futures trades at 8347 while the spot is at 8340. Futures would have a delta value of 1. We know that for every 1 point change to the underlying futures, the futures will also change by 1 point.

Let's say I buy one ATM option with a delta of 0.50. This means that every 1 point in the underlying, the option moves by 0.5. The other way around is that owning one ATM option is equivalent to holding half a futures contract. This means that if I have 2 of these ATM contracts, it is as good as having 1 futures contract. The delta of the 2 ATM options, i.e. The total delta is 1! To sum up, the total delta for the position can be calculated by adding the deltas from two or more option contract.

Let's look at some case studies to better understand the situation.

Case 1: Nifty spot at 8125, trader can choose from 3 Call options (CHART)

Observations

1. The Position Delta column shows a positive sign beside 1 that indicates a 'long' position.
2. The sum of the positions has a positive delta, i.e. +1.25 This means that both the underlying position and the combined position move in the same direction.
3. Each 1 point increase in Nifty results in a 1.25-point change to the combined position
4. If the Nifty moves 50 points, then the combined position will move 50 * 1.25 = 62.5 Points

Case 2: Nifty spot at 8125. Trader has a combination Call and Put options.
(CHART

Observations

1. The sum of the positions has a positive delta, i.e. +0.25. The underlying position and combined position both move in the same direction.
2. The overall position delta has been reduced by the addition of DeepITM PE. This means that the position combined is less sensitive the the directional movements of the market.
3. Each 1 point increase in Nifty results in a 0.25 point change to the combined position
4. If the Nifty moves 50 points, then the combined position will move 50 * 0.25 = 12.5 Points
5. Important note: Deltas can be added to calls and puts as long as they belong to the same underlying.

Case 3 - Trader holds Nifty spot at 8125 and has a mix of Call and Put options. Here, he has two lots of Put options.

(CHART)

Observations

1. The sum of the positions has a positive delta, i.e. +0.25. The underlying position and combined position both move in the same direction.
2. The overall position delta has been reduced by the addition of DeepITM PE. This means that the position combined is less sensitive the the market's directional movements.
3. Each 1 point increase in Nifty results in a 0.25 point change to the combined position
4. If the Nifty moves 50 points, then the combined position will move 50 * 0.25 = 12.5 Points
5. Important note: Deltas can be added to calls and puts as long as they belong to the same underlying.

Case 3 - Trader holds Nifty spot at 8125 and has a mix of Call and Put options. Here, he has two lots of Put options.

Observations

1. The 8100 CE (ATM), has a positive delta value of +0.5
2. The ATM 8100 PE has a negative delta value of -0.5
3. The delta of the combined position is 0. This means that it doesn't get affected by any changes in the underlying
1. For example, if Nifty moves 100 points, then the change in options positions will be 100 * 0. = 0
4. These positions, which have a combined Delta of 0, are also known as 'Delta Neutral’ positions
5. Any directional change does not affect Delta Neutral positions. They act as though they are shielded from market movements
6. But, Delta neutral positions react to other variables such as Volatility or Time. Later,we will discuss this.

Case 5: Nifty spot at 8125. Trader sold a Call Option
(CHART

Observations

1. The Position Delta column shows a negative sign beside 1 that indicates a'short position'.
2. A short call option can cause a negative delta, which means that the option position and the underlying move are in opposite directions. This is quite obvious considering that an increase in spot price results in a loss for the seller of the call option.
3. The delta also turns positive if you short the PUT option
1. -1 * = +0.5

Let's take, for example, a trader who has five lots of deep ITM options. The total delta for such a position would be +5 * +1 = +5. This means that for every 1 point in the underlying position change, the combined position would change 5 points in the opposite direction.

You can achieve the same result by reducing 5 deep ITM Put options.

- 5 * 1 = +5

-5 indicates 5 short positions, and -1 the delta of deep ITM Put Options.

These case studies can give an overview of the steps required to add up deltas at individual positions and calculate a total delta. This method can be extremely useful when there are many positions to choose from and you want to determine the overall effect of the positions on direction.
Keep in mind the another important point -

To be more accurate, I strongly suggest that you add the deltas to each position to gain a perspective. This will help you understand the sensitivity as well as the leverage of your overall position.

Another important point to keep in mind is -

Delta of ATM Option = 0.5

If you have two ATM options, the delta of your position is 1.

The overall position changes by 1 point for every change in the underlying. This is because the delta is 1. This option is able to mimic the movement of Futures contracts. These two options are not meant to be used as a substitute for futures contracts. The direction of the market is the only factor that affects the Futures contract, but other variables can have an impact on options contracts.

You might choose to substitute futures for options contracts at times (mainly from a margins perspective). We will discuss these implications in more detail as we go.

## 11.2 - Delta - A probability

Here's another interesting use of Delta before we end our discussion about Delta. The Delta can be used to determine the likelihood that the option contract will expire in the money.

Let me clarify: When a trader purchases an option, regardless of whether it is Calls or Puts, what does he aim for? What do you expect if you buy Nifty 8100 PE while the spot is trading at 8100, for example? Note that 8000 PE is an OTM Option. We expect the market will fall so that our Put option can make money.

The trader actually hopes that the spot price drops below the strike price so the option switches from OTM to ITM option. In this way, the premium goes up and the trader earns more.

To determine the likelihood of the option being converted from OTM into ITM, the trader can use delta.

The example of 8000 PE is slightly OTM; therefore, its delta must not be below 0.5. Let us change it to 0.3 for the sake this discussion.

To calculate the probability that the option will be offered to change from OTM to ITM you can convert the delta into a percentage number.

Delta of 0.3 equals 30% when converted into percentage terms. Therefore, there is only a 30% chance that the 8000 PE will become an ITM option.

You find that interesting? This is quite interesting, right?

1. 8400 CE trades at Rs.4/
2. Spot trading is at 8275
3. You have two days to expire - would this be a good time for you to buy this option?

A typical trader would believe that this trade is low-cost. After all, the premium is only Rs.4/- so there is nothing to lose. The trader might even believe that if the trade goes in his favor, there is a chance to make huge profits.

This is the way options work. Let's pretend to be 'Model Thinking' and see if it makes sense.

1. 8400 CE is a deep OTM call option, considering spot is at 8275
2. This option's delta could be as low as 0.1
3. Delta says that the possibility of ITM expiring is 10%
4. The fact that the option is valid for only two more days makes the case for purchasing this option even stronger.

This option would not be purchased by a prudent trader. But don't think it would make sense to sell the option and get the premium? You should consider this: there is only 10% chance that the option will expire ITM, or in other words, there is 90% chance that the option will expire as an OTM option. You should be confident about the trade, as there is a high probability that the seller will win.

The same question can be asked about the delta of ITM options. Nearly 1 right? This means that there is a high chance for an ITM option already expired to become ITM. This means that the likelihood of an ITM option expiring OTM as ITM is low. So be careful when shorting/writing ITM options, the odds are already against your side!

Smart trading is about making trades that are in your favor. To know the odds of winning, you need to be able to see your numbers and use your "Model Thinking" hat.

I trust you now have a good understanding of the first Option Greek - The Delta.

We are beckoned by the Gamma now.

### keypoints-

1. Nature is rich in the delta.
2. A futures contract's delta is always 1.
3. Two ATM options are equivalent to 1 futures contract
4. The options contract does not serve as a surrogate for futures contracts.
5. The probability that an option will expire ITM is the delta of an option.