Professional Trading through Option Theory

Lesson -> Delta - Section 2

10.1-Consider the Model Thinking

You were given a glimpse into the first option Greek, the Delta. The previous chapter did not only discuss the delta but also had a hidden agenda - to guide you along a path of'model thinking. Let me clarify what I mean. The previous chapter opened up new opportunities to evaluate options. You will no longer view options from a single perspective thanks to the window.

If you are bullish on the markets, you might not plan your trades this way.

You may prefer to strategize in this manner: "My view is bullish, as I expect the markets to move by 40 Points. Therefore it makes sense for me to buy options with a delta of at least 0.5 as the option is expected gain at most 20 points for that 40 Point move in the market."

Can you see the differences between these two thought processes? The former may seem a little naive and casual while the latter is more structured and quantitative. We discussed in the previous chapter how the expectation of a 20-point move in the option premium resulted from a formula.

Expected Change in Option Premium = Option Delta * Points Change in the Underlying

This is only one part of the overall game plan. The trade selection process becomes easier and more scientifically-sound as we uncover the other Greeks. The point is that the future thinking will be guided by numbers and equations, and "casual trading thoughts" will have very limited scope. There are many traders who trade with just a few random thoughts, and some of them may be successful. This is not for everyone. You can make better odds by putting numbers in perspective. This is what happens when you use'model thinking.

Keep in mind the model thinking framework when analyzing options. This will help you to set up systematic trades.

10.2 - Delta against the spot price

We have already discussed the importance of Delta, and how it can be used to estimate the premium change. Let's start by reviewing the last chapter.

  1. Call options have a +ve Delta. A delta value of 0.4% means that for every 1 point increase or loss in the underlying call options premium gains/losses 0.4 points will be added/reduced . 
  2. A put option has a delta of -0.4. A put option with a delta -0.4 means that for every 1 point in the underlying, the premium gains/losses 0.4%
  3. OTM options have a Delta value between 0 to 0.5, ATM option has an average delta of 0.5, while ITM option has an average delta between 0.5-1.

Let me draw some conclusions from the 3 rd points. Let's say Nifty Spot is at 8320, the strike is 8400, and the option type is CE (Call Option, European).

  1. How much is the Delta value of the 8400 CE if the spot is 8312 and the CE is 8400 CE?
    1. Delta should be between 0.50 and 0.5 since 8400 CE is OTM. Let's assume that Delta is 0.
  2. What do you think the Delta value is if Nifty spot moves between 8312 and 8400?
    1. Delta should be about 0.5, as the ATM option of 8400 CE now offers Delta
  3. Let's say that Nifty spot moves between 8400 and 8500. What do you think the Delta value is?
    1. Delta should be closer than 1 since the 8400 CE is an ITM option. Let's say 0.8.
  4. Let's say Nifty Spot cracks and falls to 8300 from 8500. What happens to delta?
    1. The option has been made an OTM again from ITM due to the fall in spot. Therefore, delta's value falls from 0.8 down to 0.35.
  5. What can you draw from these 4 points?
    1. As and when the spot price changes, the moneyness and thus the delta of an option change.

This is an important point: The delta changes with changes to spot. Delta is therefore a variable, not a fixed entity. If an option has a delta value of 0, it is likely that the value will change as the underlying value changes.

The chart below shows the delta movement versus spot price. This chart is generic and does not include any specific strike or option. You can see that there are two lines.

  1. The blue line shows the delta behavior of Call options (varies between 0 and 1)
  2. The delta behavior of the Put option (varies between -1 and 0) is captured by the red line.

Let's get to know this better. (IMAGE 1)

This chart is very interesting. I suggest that you only focus on the blue line, and completely ignore the red. The delta of a call options is represented by the blue line. The graph below shows a few interesting characteristics of delta. Let me briefly list them (while you're doing so, keep in mind that as the spot price changes, so does the option's moneyness).

  1. Take a look at the X-axis. As the spot price crosses from OTM to ATM, ITM to ITM, the moneyness of starting from left increases.
  2. The delta line (blue) is a measure of spot price changes. As such, the delta line increases.
  3. OTM's delta is near 0 at OTM - this means that regardless of the spot price falling (going from OTM deep OTM), the option's delta will still be at 0
    1. Keep in mind that the delta of a call option is lower bound than 0
  4. The delta increases when the spot moves from OTM ATM (remember that the option's moneyness also goes up).
    1. You can see that the delta of options is within 0 to 0.25 range for options less than ATM
  5. The delta at ATM reaches a value of 0.
  6. The delta begins to move beyond the 0.5 mark when the spot moves from the ATM towards ITM.
  7. When the value of 1 is reached, you will notice that the delta begins to fatten up.
    1. This means that the delta value doesn't change if the delta moves beyond ITM, or deep ITM. It remains at its value of 1 max.

Similar characteristics can be observed for the Put Option's Delta (red line).

10.3 - Understand The Delta Acceleration

You may have heard bizarre stories about traders who trade OTM options, doubling or tripling their income. I'm sure you have heard of such stories. It was the 17th th Mai 2009 (Sunday), when the election results were announced, and the UPA Government was re-elected at center. Dr. Manmohan Singh returned as Prime Minister to complete his 2 nd term. Stock markets love stability at the centre and we knew that the market would rise the next day, i.e. 18 The May 2009. Nifty closed at 3671 the day before.

Zerodha wasn't born that day. We were just traders trading our capital with a few clients. A few days before 17 th May, one of our associates took a big risk and bought far-off options (OTM) for Rs.200,000/-. This was a daring devil act considering that no one can predict the outcome of general elections. He would be able to benefit from a rally in the market, but there are many factors that must be considered for the market's success. We were also anxious to see what would happen. Final results were announced and everyone knew that he would make some money on the 18 th May, but we didn't know how much.

18 The May 2009 was a day I will never forget. Markets opened at 9:55AM (that was market opening time back then). It was a huge bang open for the market. Nifty immediately hit an up circuit and markets froze. Nifty rose close to 20% in a matter of minutes to close the day at 4321. Because the market was too hot, the exchanges closed it at 10:01 AM. It was also the longest working day I have ever had.

This chart highlights the market's movement for that day.

Our dear associate had made a lot of money throughout the entire process. His options were valued at Rs.28,000.00/- an incredible 1300% gain in just a few hours. These are the trades almost every trader wants to do.

Let me ask you some questions about this story, and then we'll get back to the main subject -

  1. Why would you believe that our associates choose OTM options over ATM or ITM options?
  2. What would have been the outcome if he had purchased an ITM option or an ATM option?

These graphs provide the answer to your questions.
(IMAGE 3).

This graph discusses the 'Delta Acceleration.' There are four stages in this graph. Let's look at each one.

Let's start the discussion by highlighting some important points.

  • The following points are important to remember and pay attention to.
  • Recall the last chapter's delta table and revise it (option type, approximate value, etc.).
  • Keep in mind that the premium and delta numbers are an intelligent assumption.

Predevelopment This stage is when OTM or deep OTM is available. Here, the delta is very close to 0. Even if the option is moved from deep OTM into OTM, the delta will still be close to 0. If spot is 8400, 8700 call option is Deep OTM. This is likely to have an average delta of 0.05 Even though the spot is moving from 8400 to 8500, the delta for 8700 Call Option will not change much since 8700 CE remains an OTM option. The delta will remain a small, non-zero number.

If the premium for 8700 CE spot at 8400 is Rs.12 then the premium will likely move 100 * 0.05 = 5 points when Nifty moves up to 8500 (100-point move).

The new premium will now be Rs.12 + 5, which is Rs.17/-. The 8700 CE is considered to be slightly OTM, but not deep OTM.

Important to note is that while the absolute change in premium value may be small (Rs.5/), the percentage option of Rs.12/ has increased by 41.6% to reach Rs.17/-

Conclusion Deep OTM options can put on a high percentage but it must move by a large amount.

Recommendation: Avoid buying deep-OTM options. The deltas are small and the underlying must move rapidly for the option to work for you. You can get more bang for your buck elsewhere. Selling deep OTM is a good idea. However, we will assess when to sell these options once we have the Greek 'Theta.

Takeoff & Acceleration This is where the option switches from OTM to ATM. This stage is where you get the most bang for your buck and the highest risk.

This is how it looks: Nifty spot @ 8400 CE, strike is 8500 CE, option slightly OTM, delta 0.25, premium Rs.20/-

Spot changes between 8400-8500 (100 point), but to see what happens in premium side, let us do the math .

Change in the underlying = 100

Delta for 8500 CE = 0.25

Premium change =
100 * 0.25 = 25

New premium = Rs.20 + Rs.25 = Rs.45/

Percentage Change = 125%

Can you see it? OTM options can behave very differently for the same 100-point move.

Conclusion The slightly OTM option, which has a delta value between 0.2 and 0.3, is more sensitive to changes within the underlying.It is impressive to see the percentage change in OTM options for any significant changes in the underlying. Option traders can thus double or triple their income by buying slightly OTM options. They buy OTM options if they expect big moves in the underlying. This is just one aspect of the cube. There are many other aspects of the cube to explore

Recommendation: Although slightly OTM options are more expensive than deep OTM options you can still make a lot of money if your plan is well executed. Consider buying OTM options if you are considering options. We will discuss this later, but it is worth looking at if there is still time for them to expire.

Let's move on and see what the ATM option does for the same 100-point move.

Spot = 8400

Strike = 8400 (ATM).

Premium = Rs.60/-

Change in the underlying = 100

Delta for 8400 CE = 0.5

Premium change =
100 * 0.5 = 50

New premium = Rs.60 +50 = Rs.110/

Change in percentage = 83%

Conclusion –ATM options have a greater sensitivity to spot changes than OTM options. Because the ATM's delta value is high, the underlying does not need to move by a large amount. Even though the underlying is moving by a small amount, the option premium will change. OTM options are cheaper than ATM options, but ATM options can be more expensive to buy.

Recommendation:Buy ATM Options when you want to be safe. Even if the underlying moves by a significant amount, the ATM option will still move. As a corollary to this, don't attempt to sell an ATM option until you are certain about your actions.

Stabilization When the option switches from ATM to ITM or Deep ITM, the delta stabilizes at 1. The graph shows that the delta begins to flatten when it reaches 1. This means that the option could be deep ITM or ITM, but the delta would remain fixed at 1 and not change.

Let's see how it works.

Nifty Spot = 8400

Option 1 = 8300 CE Strike ITM option, Delta 0.8, Premium Rs.105

Option 2 = 8200 CE Strike and Deep ITM Option. Delta of 1.0. Premium is Rs.210

Change in the underlying = 100 points. Nifty then moves to 8500.

Let's now see how these two options perform -

Premium change for Option 1 = 100 *0.8 = 80

New Premium for Option 1 = Rs.105 + Rs.80 = Rs.185/

Percentage change = 80/105 = 76.9%

Premium change for Option 2 = 100 1 = 100

New Premium for Option 2 = Rs.210 +100 = Rs.310/

Percentage change = 100/210 = 46.6%

Conclusion The deep ITM option is better than the slightly ITM option in terms of absolute changes in the number points. It is not the opposite in terms of percentage changes. ITM options are clearly more sensitive to changes in the underlying, but they are also the most expensive.

Notice the difference in the deep ITM option delta 1. For every 100 points change in the underlying, there is an increase in the option premium by 100. This basically means that a deep ITM choice is just as good as the underlying. The reason is that no matter what the underlying changes, the option premium will also change.

RecommendationBuy ITM options if you want to be very safe.let's contrast the deep OTM with ITM(Option). Delta is a characteristic of ITM options that are sensitive to changes in the underpinning.

The Deep ITM option is in line with the underlying. This means that you can replace a deep ITM option with a futures contract.

This is how you should think about it -

Nifty Spot @8400

Nifty Futures = 84909

Strike = 8000 (deeper ITM)

Premium = 450

Delta = 1.0

Spot change = 30 points

New Spot value = 8430

Futures Change = 8409 + 30 = 84339 a This represents the total 30 point change

Change Option Premium = 1*30 = 30

New Option Premium = 30 +450 = 480 A Reflects the whole 30 point increase

The point is that futures and deep ITM options respond very similarly to changes in the underlying. You will be able to reduce your margin burden by purchasing a Deep ITM option. If you do decide to buy a Deep ITM option, however, you must ensure that it remains Deep ITM (in other terms, make sure the delta stays at 1) and keep an eye on the contract's liquidity.

If you're just starting to explore the Greeks, I think this chapter might be a bit too much. This information should be taken slowly.

We have a few more angles to consider with regard to the delta. But that will be covered in the next chapter. Let's summarize the discussion using a table before we close this chapter.

This table will allow us to understand how different options react to changes in the underlying.

Bajaj Auto has been my underlying. Bajaj Auto is expected to reach 2240 at the current price of 2210. The expectation is for a 30 point increase in the underlying. We also believe that there will be plenty of time for the contract to expire, so time is not a concern.

As you can see, each option reacts differently to the same move in underlying.

Before I close this chapter, I told you a story that I had previously shared with you. I then posted a few questions. You might be able to go back and answer the questions.


  1. Model Thinking is a science-based approach to trading that uses scientifically-based models.
  2. The spot value changes and the Delta changes, so the Delta will change.
  3. The delta changes with the transition from OTM to ATM and ITM as the option becomes ITM.
  4. Delta reaches a value of 0.50 for ATM options
  5. When the option switches from Deep OTM into OTM, it is called delta predevelopment.
  6. Delta Takeoff and Acceleration is when the option switches from OTM to ATM
  7. When the option switches from ATM to ITM or Deep ITM, it is called delta stabilization
  8. High % returns are often attained by buying options during the takeoff stage.
  9. The option to buy Deep ITM is just as good as the option to purchase the underlying.