Module 5 Options Theory for Professional Trading

Chapter 11

Delta (Part 3)



11.1 – Add up the Deltas

Here is an interesting characteristic of the Delta – The Deltas can be added up!

Let me explain – we will go back to the Futures contract for a moment. We know for every point change in the underlying’s spot value the futures also changes by 1 point. For example if Nifty Spot moves from 8340 to 8350 then the Nifty Futures will also move from 8347 to 8357 (i.e. assuming Nifty Futures is trading at 8347 when the spot is at 8340). If we were to assign a delta value to Futures, clearly the future’s delta would be 1 as we know for every 1 point change in the underlying the futures also changes by 1 point.

Now, assume I buy 1 ATM option which has a delta of 0.5, then we know that for every 1 point move in the underlying the option moves by 0.5 points. In other words owning 1 ATM option is as good as holding half futures contract. Given this, if I hold 2 such ATM contracts, then it as good as holding 1 futures contract because the delta of the 2 ATM options i.e. 0.5 and 0.5, which adds up to total delta of 1! In other words the deltas of two or more option contracts can be added to evaluate the total delta of the position.

Let us take up a few case studies to understand this better –

Case 1 – Nifty spot at 8125, trader has 3 different Call option.

Sl No Contract Classification Lots Delta Position Delta
1 8000 CE ITM 1 -Buy 0.7 + 1 * 0.7 = + 0.7
2 8120 CE ATM 1 -Buy 0.5 + 1 * 0.5 = + 0.5
3 8300 CE Deep OTM 1- Buy 0.05 + 1 * 0.05 = + 0.05
Total Delta of positions = 0.7 + 0.5 + 0.05 = + 1.25

Observations –

  1. The positive sign next to 1 (in the Position Delta column) indicates ‘Long’ position
  2. The combined positions have a positive delta i.e. +1.25. This means both the underlying and the combined position moves in the same direction
  3. For every 1 point change in Nifty, the combined position changes by 1.25 points
  4. If Nifty moves by 50 points, the combined position is expected to move by 50 * 1.25 = 62.5 points

Case 2 – Nifty spot at 8125, trader has a combination of both Call and Put options.

Sl No Contract Classification Lots Delta Position Delta
1 8000 CE ITM 1- Buy 0.7 + 1*0.7 =0.7
2 8300 PE Deep ITM 1- Buy – 1.0 + 1*-1.0 = -1.0
3 8120 CE ATM 1- Buy 0.5 + 1*0.5 = 0.5
4 8300 CE Deep OTM 1- Buy 0.05 + 1*0.05 = 0.05
Total Delta of positions  0.7 – 1.0 + 0.5 + 0.05 = + 0.25

Observations –

  1. The combined positions have a positive delta i.e. +0.25. This means both the underlying and the combined position move in the same direction
  2. With the addition of Deep ITM PE, the overall position delta has reduced, this means the combined position is less sensitive to the directional movement of the market
  3. For every 1 point change in Nifty, the combined position changes by 0.25 points
  4. If Nifty moves by 50 points, the combined position is expected to move by 50 * 0.25 = 12.5 points
  5. Important point to note here – Deltas of the call and puts can be added as long as it belongs to the same underlying.

Case 3 – Nifty spot at 8125, trader has a combination of both Call and Put options. He has 2 lots Put option here.

Sl No Contract Classification Lots Delta Position Delta
1 8000 CE ITM 1- Buy 0.7 + 1 * 0.7 = + 0.7
2 8300 PE Deep ITM 2- Buy -1 + 2 * (-1.0) = -2.0
3 8120 CE ATM 1- Buy 0.5 + 1 * 0.5 = + 0.5
4 8300 CE Deep OTM 1- Buy 0.05 + 1 * 0.05 = + 0.05
Total Delta of positions 0.7 – 2 + 0.5 + 0.05 = – 0.75

Observations –

  1. The combined positions have a negative delta. This means the underlying and the combined option position move in the opposite direction
  2. With an addition of 2 Deep ITM PE, the overall position has turned delta negative, this means the combined position is less sensitive to the directional movement of the market
  3. For every 1 point change in Nifty, the combined position changes by – 0.75 points
  4. If Nifty moves by 50 points, the position is expected to move by 50 * (- 0.75) = -37.5 points

Case 4 – Nifty spot at 8125, the trader has Calls and Puts of the same strike, same underlying.

Sl No Contract Classification Lots Delta Position Delta
1 8100 CE ATM 1- Buy 0.5 + 1 * 0.5 = + 0.5
2 8100 PE ATM 1- Buy -0.5 + 1 * (-0.5) = -0.5
Total Delta of positions + 0.5 – 0.5 = 0

Observations –

  1. The 8100 CE (ATM) has a positive delta of + 0.5
  2. The 8100 PE (ATM) has a negative delta of – 0.5
  3. The combined position has a delta of 0, which implies that the combined position does not get impacted by any change in the underlying
    1. For example – If Nifty moves by 100 points, the change in the options positions will be 100 * 0 = 0
  4. Positions such as this – which have a combined delta of 0 are also called ‘Delta Neutral’ positions
  5. Delta Neutral positions do not get impacted by any directional change. They behave as if they are insulated to the market movements
  6. However Delta neutral positions react to other variables like Volatility and Time. We will discuss this at a later stage.

Case 5 – Nifty spot at 8125, trader has sold a Call Option

Sl No Contract Classification Lots Delta Position Delta
1 8100 CE ATM 1- Sell 0.5 – 1 * 0.5 =  – 0.5
2 8100 PE ATM 1- Buy -0.5 + 1 * (-0.5) = – 0.5
Total Delta of positions – 0.5 – 0.5 = – 1.0

Observations –

  1. The negative sign next to 1 (in the Position Delta column) indicates ‘short’ position
  2. As we can see a short call option gives rise to a negative delta – this means the option position and the underlying move in the opposite direction. This is quite intuitive considering the fact that the increase in spot value results in a loss to the call option seller
  3. Likewise if you short a PUT option the delta turns positive
    1. -1 * (-0.5) = +0.5

Lastly just consider a case wherein the trader has 5 lots long deep ITM option. We know the total delta of such position would + 5 * + 1 = + 5. This means for every 1 point change in the underlying the combined position would change by 5 points in the same direction.

Do note the same can be achieved by shorting 5 deep ITM PUT options –

– 5 * – 1 = + 5

-5 indicate 5 short positions and -1 is the delta of deep ITM Put options.

The above case study discussions should give you a perspective on how to add up the deltas of the individual positions and figure out the overall delta of the positions. This technique of adding up the deltas is very helpful when you have multiple option positions running simultaneously and you want to identify the overall directional impact on the positions.

In fact I would strongly recommend you always add the deltas of individual position to get a perspective – this helps you understand the sensitivity and leverage of your overall position.

Also, here is another important point you need to remember –

Delta of ATM option = 0.5

If you have 2 ATM options = delta of the position is 1

So, for every point change in the underlying the overall position also changes by 1 point (as the delta is 1). This means the option mimics the movement of a Futures contract. However, do remember these two options should not be considered as a surrogate for a futures contract. Remember the Futures contract is only affected by the direction of the market, however the options contracts are affected by many other variables besides the direction of the markets.

There could be times when you would want to substitute the options contract instead of futures (mainly from the margins perspective) – but whenever you do so be completely aware of its implications, more on this topic as we proceed.

11.2 – Delta as a probability

Before we wrap up our discussion on Delta, here is another interesting application of Delta. You can use the Delta to gauge the probability of the option contract to expire in the money.

Let me explain – when a trader buys an option (irrespective of Calls or Puts), what is that he aspires? For example what do you expect when you buy Nifty 8000 PE when the spot is trading at 8100? (Note 8000 PE is an OTM option here). Clearly we expect the market to fall so that the Put option starts to make money for us.

In fact the trader hopes the spot price falls below the strike price so that the option transitions from an OTM option to ITM option – and in the process the premium goes higher and the trader makes money.

The trader can use the delta of an option to figure out the probability of the option to transition from OTM to ITM.

In the example 8000 PE is slightly OTM option; hence its delta must be below 0.5, let us fix it to 0.3 for the sake of this discussion.

Now to figure out the probability of the option to transition from OTM to ITM, simply convert the delta to a percentage number.

When converted to percentage terms, delta of 0.3 is 30%. Hence there is only 30% chance for the 8000 PE to transition into an ITM option.

Interesting right? Now think about this situation – although an arbitrary situation, this in fact is a very real life market situation –

  1. 8400 CE is trading at Rs.4/-
  2. Spot is trading at 8275
  3. There are two day left for expiry – would you buy this option?

Well, a typical trader would think that this is a low cost trade, after all the premium is just Rs.4/- hence there is nothing much to lose. In fact the trader could even convince himself thinking that if the trade works in his favor, he stands a chance to make a huge profit.

Fair enough, in fact this is how options work. But let’s put on our ‘Model Thinking’ hat and figure out if this makes sense –

  1. 8400 CE is deep OTM call option considering spot is at 8275
  2. The delta of this option could be around 0.1
  3. Delta suggests that there is only 10% chance for the option to expire ITM
  4. Add to this the fact that there are only 2 more days to expiry – the case against buying this option becomes stronger!

A prudent trader would never buy this option. However don’t you think it makes perfect sense to sell this option and pocket the premium? Think about it – there is just 10% chance for the option to expire ITM or in other words there is 90% chance for the option to expire as an OTM option. With such a huge probability favoring the seller, one should go ahead and take the trade with conviction!

In the same line – what would be the delta of an ITM option? Close to 1 right? So this means there is a very high probability for an already ITM option to expire as ITM. In other words the probability of an ITM option expiring OTM is very low, so beware while shorting/writing ITM options as the odds are already against you!

Remember smart trading is all about taking trades wherein the odds favor you, and to know if the odds favor you, you certainly need to know your numbers and don your ‘Model Thinking’ hat.

And with this I hope you have developed a fair understanding on the very first Option Greek – The delta.

The Gamma beckons us now.

Key takeaways from this chapter

  1. The delta is additive in nature
  2. The delta of a futures contract is always 1
  3. Two ATM option is equivalent to owning 1 futures contract
  4. The options contract is not really a surrogate for the futures contract
  5. The delta of an option is also the probability for the option to expire ITM


  1. khyati verdhan says:

    Hi kartik
    Very very thanks for this chapter.This is very intresting chapter, but after reading this a no. of things running in my mind. Please check this and correct me where I am wrong.
    If delta (sum of all delta’s) is
    1. +1.75
    Profit- when market goes up
    Loss – when market goes down
    2. +.025
    Profit- when market goes up
    Loss – when market goes down
    3. 0
    No profit , No loss at any market movement
    4. -.075
    Profit- when market goes down
    Loss – when market goes up

    I also think to calculate net p&l , I can do it mathematically-
    Net P&L= total no. of shares of same underlying * change in underlying *total delta(sum of all delta’s)
    • Profit- when market goes up and delta is +ve
    When market goes down and delta is –ve
    • LOSS- when market goes up and delta is -ve
    When market goes down and delta is +ve

    Is this formula correct??? Since delta is also variable , I am confused. Please clarify

    • Karthik Rangappa says:

      You are absolutely right here –

      1) If the deltas add up to a +ve number, this means you make money when the markets goes up
      2) If the deltas add up to a -ve number, this means you make money when the markets goes down
      3) Net P&L = Change in underlying * Total Delta * Lot size —-> how ever please do bear in mind this is only an expected P&L and not really the actual P&L. Remember an options contract is subjected to other variables…we will understand this point in detail over the subsequent chapters.

  2. NARSIMHA says:

    sir,in tradinr intraday or swing what is definition of down &uptrenr i mean how many candeles down,up

  3. jagadeesh says:

    Yet another great article.. Thanks for this.. 🙂

    • Karthik Rangappa says:

      I must thank you for patiently reading all the articles on Varsity and constantly encouraging us 🙂

  4. kieron says:

    Thank you sir salute you for an great article

  5. kavyasalunke says:

    sir i have doubt regarding stoploss of option order,if i want to place stop loss for option with repect to it’s underlying how can i calculate it? also if option expiring as otm but if my premium is changed by 4-5 what should i consider it means profit or I had paid premium after profit?

    • Karthik Rangappa says:

      This is a very valid question – in fact I would explain this in detail when we take up the 3rd option Greek – Vega. So request you to please stay tuned till then. Thanks.

  6. khyati verdhan says:

    Hi kartik,
    Thanks for clearing my confusions.I have read the chapter many times and develops a clear concept. Clearly, options are superior than futures. But, thinks problems me is- if ‘X’ persons trade nifty futures, he has to trade at nifty future prices but if ‘Y’ persons trade nifty options and there are 10 strike prices available , then each strike price has only Y/10 volume. However, ATM options are somehow more volume. Then is there any volume issue with options. Please clarify.

    • Karthik Rangappa says:

      I get your point here, in fact for this reason along with many others ATM options are always a good option to trade. You will understand more on this as we progress.

  7. keshav says:

    I am eagerly waiting for option strategies.. When will u complete this module..?
    When will u upload next chapter..?

    • Karthik Rangappa says:

      Chapter 12 about Gamma (Part 1) should be up by t’row – it is a very different chapter and hopefully you will enjoy reading it 🙂

  8. ALOK says:

    Worth it…Nice job i appreciate your efforts.

  9. arshad says:

    I have spent lots of money for getting training about but all are worthless as compare to Varsity….u all did a great job..thanks..

    • Karthik Rangappa says:

      Thanks Arshad.

      There are many so called ‘market educators’ who in the pretext on teaching market finance fleece your hard earned money. Keeping this in perspective we started Varsity with an objective of creating an online platform where we put up meaningful content and make it available for everyone, for free.

  10. Ajay says:


    I recently read about the Adani enterprise demerger and the controversy surrounding it s the stock plunged 80% intraday. How does it impact the a) market lot b) futures price c) premium?

    • Karthik Rangappa says:

      Adani was a mess – mostly attributable to people not reading the circular issued by NSE. The lot size/Future Price/Premium all depends on the corporate action in perspective. However they all reduce or increase in proportion to the spot value.

  11. Ramesh says:

    Hi Team,
    Great articles/modules. I’ve learn’t a lot here than reading/attending classes. Very well writen with lots of examples. Thank you very much.
    A lay man question: In delta lesson modul, you’d mentioned that +5 delta moves by 5 points the underling movement of 1 point. Are you refering to points as in ‘premium change’? Pleae kindly clarify.

    • Karthik Rangappa says:

      Thanks Ramesh, very happy to know that you appreciate the efforts. Please do stay tuned for more.

      Yes, if an option has a Delta of 0.5, then for every 1 point change in the underlying then the premium changes by 0.5 points.

      • Ramesh says:

        Thank You Karthik.
        So if 5 contracts of 0.5 Delta then, the Delta adds up to 2.5. Then every 1 point move in underlying the position will now move 2.5 times (premium points) – either side up or down.

  12. Sanatharam says:

    Can I use option strategies for intraday trading depending upon the situation? In intraday for example if am using bull spread, the shorted OTM Option won’t have much impact due to non deterioration of theta.. Even the Usage of neutral strategy, shorting 2ATM, Buying 1ITM & 1OTM won’t have much impact if my position is wrong.. Suggest the usage of options strategy for intraday trading…

    • Karthik Rangappa says:

      Sanatharam…I will be discussing options strategies in detail in the next module. Request you to kindly stay tuned.

  13. Susanta says:

    Hi, thanks for the all teaching modules.. I understand that Delta for call option is +ve, and delta for Put option is -ve. I have a question.. Can delta be a negative value for a only call option ? I assume not.. But still have a confusion.

    • Karthik Rangappa says:

      Call Delta per say is a +ve number, but when you short a call option the Delta is considered -ve. Similarly when you short a put option the delta is considered +ve.

  14. Anand Singh says:

    Hi Karthik, I didn’t understand the case no #5 in this chapter. Can you please elaborate this with premium, delta values for better understanding. Thanks in advance

    • Karthik Rangappa says:

      Anand – Case 5 talks about a situation wherein you have a short ITM Call option. ITM options have a delta of 0.5, since you are short call option the position delta would be 1 * (-0.5) = -0.5. The other position is a long ITM Put option. Put option has a negative delta…but do remember when you short a put option, the delta is +ve.

      So the overall delta of this position becomes -0.5 (from short ITM call) plus -0.5 (from long ITM Put), hence an over all delta of -1.0.

      • Anand Singh says:

        Sir, It is ATM position as delta is 0.5. Correct Sir.

        • Karthik Rangappa says:

          Yup….in and around 0.5.

          • Anand Singh says:

            Thanks Karthik. I owe you a lot. Your gyan on technical analysis enriched my knowledge and ignited passion for trading. Thanks a ton. After saying goodbye to long career in banking and insurance I decided to become full time trader and was looking for authentic material on TA and FA. Believe me your content is far more better than any book on share market in circulation. Karthik tell me is it true that 95% people loose money in the market. If it is true then who are the rest 5%. And how to increase the success rate in trading. Plz share your thoughts.

          • Karthik Rangappa says:

            Thanks for the kind words Anand. Yes, it is true that most of the people lose money ‘attempting’ to trade. Think is mainly because the vast majority trade based on gut feel, and random theories. Besides somewhere their egos take over their brains and they fail to evolve themselves as traders. Most of them dont even bother to educate themselves.

            My suggestion – Stay humble and constantly educate yourself. This alone will enhance your odds of being successful in the markets.

  15. lalitdimple says:

    Dear Mr. Karthick,
    Greetings the day.
    I have just joined Zerodha in Nov’15 and was going through varsity modules. Actually, I was shocked to note that there is someone who has such a practical and simple way of teaching. Definitely, this is only experience and involvement which speaks. I have gone upto Thetha chapter only, which has been the simplest chapter for me.
    I just had a query and no one else can be better than you to address it. I am extremely sorry for disturbing you.
    Suppose nifty is trading at 8000
    I buy one Call @8000. Second @7900 and third @ 7800 so these call will be ATM, ITM and DITM.
    Suppose their Premium is 60, 80 and 100 respectively (average premium 80 ) and Delta is 0.5, 0.6 and 0.8
    As per your module, Delta of same underlying can be added hence total Delta will be 1.90
    Suppose nifty moves from 8000 to 8100 so change in underlying 8100-8000 = 100
    Change in Premium = change in underlying * Delta + old premium
    Hence 100 * 1.90 + 80
    = 190 + 80
    = 270
    Net profit = 270 – 80 ( premium paid ) * 3 ( different calls bought) * 75
    = 190 * 3 * 75
    = Rs 42750
    Or 190 * 75 = Rs 14250

    Kindly correct me. I may be wrong in adding delta or calculating new premium.

    • Karthik Rangappa says:

      Lalit – glad to know you like Zerodha Varsity 🙂

      1) Yes you can add up the deltas – this gives the overall delta of the position
      2) It would be 190 * 3 * 75 = 42750/-

      Although this seems fine to me, something tells me that we are missing something here….not able to point a finger at this moment. Will get back if it strike me 🙂

    • R. J. Keny says:

      The calculation is wrong because
      Change in uderlying 100
      Total delta 1.9
      Total premium 240
      So new premiumv = 100 x 1.9 + 240
      = 430
      Hence profit = 430 – 240 = 290

  16. lalitdimple says:

    Thanks a lot Mr. Karthik.

  17. sarath says:

    I have a doubt usd inr spot is 66.83 and 66.75 (itm)call option premium is .5075 and delta is .5 after some time spot change to 66.88 then what will be the premium and after what about spot down 66.70 please help , I am totally confused in option Greek in usd inr

    • Karthik Rangappa says:

      Delta of 0.5075 suggests that for every 1 point change in the underlying, premium will change by 0.5075. In this case the change in premium is 0.05…so the delta will change accordingly.

  18. Avinash Punjabi says:

    Hats off to You for the DELTA chapter split in to 3 parts. Every subsequent part was studied with greater enthusiam. It was a dlight.

  19. Avinash Punjabi says:

    Loved the part on DELTA as a probability of expiring ITM. Now consider the case of JAN 2016 . on 4-1-2016 the DLTA of 7500PE was .05 I assume considering the underlying price on that day, but today it’s DELTA is 0.5.
    What I wanted to know is wether we should consider the DELTA value as a probability only near expiry or mid month also as is the case today. If today closing we consider 7500PE whose DELTA is .4 ie 40%, in the next few days of fall it will become almost 0.9 and we can go wrong by writing it now. So I wanted to know how many days prior to expiry we should start considering this probability. TYour answer will be highly appreciated.

    • Karthik Rangappa says:

      Well the delta of the option indicates the probability at ‘that’ very moment. The delta helps us make a quick back of the envelop calculation on the possibility of option expiring ITM. However there is some comfort looking at this when there is very less time to expiry.

  20. ShreyaDR says:

    Agreed that option calculator gives us only theoretical values. but what is the meaning of current option price below the theoretical value or above the theoretical value.

    i have attached a screenshot here of today’s marketwatch of Nifty PE 7400 & CE 7400 along with its theoretical values in the right side. 7400PE current price is 126 which is matching with it theoretical but 7400CE cureent price is trading around 38 while it theoretical values showing it around 56. what is the meaning of this?

    • Karthik Rangappa says:

      If the current price is above or below the theoretical value, then it simply means that the option is trading higher/lower than its true worth. 7400 CE trading @ 38 while its true worth is 56 conveys the same – i.e the option is trading cheaper than its true worth. Please note, just because the option is trading cheaper you should not go ahead and buy it, be aware that it can get more cheaper after you buy.

      • ShreyaDR says:

        Yes, it is got cheaper by 4 more rupees. But is that bcoz; market is in bearish mood and the said contract is Call option? what if, the market gets reversed from this current point, will it go up to the extent and match its theoretical value?

        • Karthik Rangappa says:

          Under normal circumstances the spread between theoretical option price and market price converge. In fact it would be hard to find this spread under normal circumstance.

  21. rohit sharma says:

    Karthik, million times thanks for the hard work which you are doing for us.
    God bless you
    I have a question, regarding premium
    If you see stock of AMARAJABAT on 5 Feb, stock moved by almost 3.2% (854 on 4 Feb to 881 on 5 feb) moved by 27.5 points but premium for 850 CE (ATM on 4 Feb)did not move
    Why this happened? Sir please guide me

  22. Dhiraj Sharma says:

    Hey there, thanks for the article. I am a cfa level 2 candidate and studying option greeks from the curriculum was somewhat boresome. You have explained it all well in an easy to understand way and now I feel option greeks to be an interesting part of the curriculum and add value to my knowledge database as an option trader (though occasional) . You deserve a big thank from my side. I will recommend my pals to go through these articles.


  23. Rakesh says:

    How can i get the delta in Kite? or any other tools? i dont want to install any software. need it online

    • Karthik Rangappa says:

      As of now its not available, but we are working towards making an options suite for Kite. Hopefully this should happen soon.

  24. awesome karthik..I could not understand greeks from one of the best books on option trading by Mark D Wolfinger, but u have explained it beautifully. keep up the good work.

  25. Roji says:

    where I can get delta

  26. srividhya says:

    thank you very for your sincere efforts.. it is very simple to understand.

  27. Nil's says:

    Thnaks Karthik for the fast response. Your every response opens many close doors.

  28. garg10may says:

    When you say buying two ATM is same as buying 1 futures contract. However ATM would definitely become ITM or OTM depending on the movement and would start giving skewed returns?

    • Karthik Rangappa says:

      Yup, therefore this equation holds true only at ATM. Remember, always add up the deltas of the overall position…as long as it adds to +1 then it would equal a futures position, and there are ways to make this happen.

  29. SANDEEP REDDY says:

    How delta adding up can help, as they change with underlying.volatility also matters,right.

  30. Rakesh says:

    Hi Karthik sir,
    small doubt; can we add up the deltas of puts/calls for DIFFERENT UNDERLYINGS to know the overall position OR this procedure of adding up deltas is for only one underlying.

  31. Sai Sreedhar says:

    If the delta of a deep OTM option is 0.071, and I buy 10 Contracts of the same strike price, which makes the added up delta 0.71, does that mean I am buying an ATM/ITM option or is it still deep OTM option, just more reactive to change in underlying?

    • Karthik Rangappa says:

      Yes, you can always add up the deltas to identify the moneyness of the overall position.

      • Karthik says:

        To be more specific can we say the options are still deep OTM. It has to go through slight OTM, ATM or ITM to be profitable.

        When the options move to ATM then the moneyness at that time becomes 5 (10 * 0.5).

        • Karthik Rangappa says:

          Yes, ATM options have a delta of 0.5. The options will turn profitable once it moves from deep OTM to just OTM to ATM etc.

  32. Mrs. Shetty says:

    Read 3 chapters on Delta, but not sure whether understood it properly. its a high funda thing, will it b possible to grasp and use it.. only time will tell.
    I know not whether I fully understand it. but yet I will complete d module and then take a call whether i will be capable to trade OPTIONS.
    Great writing and explaining.

    • Karthik Rangappa says:

      Yes, please do read it. I agree it gets a bit challenging, but its worth the effort. Good luck and stay profitable.

  33. Kshitiz Sharma says:

    Hello sir I am a python and java coder(CSE student) and have been trading in Options for past 4 months with Zerodha, Is it possible for me to write a piece of code which can always generate Profit by making use of all the Greeks.
    Like I can programme taking into consideration Delta, just for intraday, because I assume the time frame can be excluded for intraday, Is it possible in reality.

    • Karthik Rangappa says:

      Hate to break you heart, but there is no code that exists that can generate profits all the time 🙂

      Codes and programming enables you and gives you better insights, but better insights does not always translates to profits.

      • Srinathjayanna says:

        Even I m a software engineer but I do prefer doing things manually wheather it is reading charts or initiating trades.Sir then don’t you do algo trades because people say it results with higher probability of winning and zerodha has streak for algo trading and don’t you use it and wats your opinion on algo trading.

        • Karthik Rangappa says:

          I’ve stopped actively trading, Srinath because I can’t devote enough time to it. However, I do invest very actively in the market. End of the day, an algo is good as the instructions you give it.

  34. varungr087 says:


    Really appreciate the way you have prepared the modules. Thank you.
    One question, At the time of buying CALL option, if we chose the strike price to be less than the underlying price then is this not equivalent to PUT option ? Why do we have so many ways to get the same thing ?

    • Karthik Rangappa says:

      No, if you buy a call option strike which is lesser than spot, then essentially you are buying an In the money call option.

  35. Swapnil says:

    Dear Karthik,
    Your articles are really very useful to us, thank you for your efforts you are putting in for us.
    I have following 2 scenarios which are I think anyone may face while trading stock options.
    1) suppose bajaj-auto spot is 2200 & I wanted to buy 2400 call option, but there are no sellers for the same. How can I buy that CE?
    2)i bought an option, On expiry my position is ITM & now i want to square off my position but no buyers are available for the same contract. What will happen to my profit in this case?
    Please clarify my doubts.
    Thank you.

    • Karthik Rangappa says:

      Well, if there are no sellers, then obviously cannot buy the shares. Hence it is important to buy/sell liquid contracts.

      Remember, if you own an option then there will certainly be a seller….so exchange will make sure that the seller will honor his obligation so that you are settled well. This is in fact one of the key roles of the exchange. Also, you maybe interested to know that our exchange systems are so robust that till date, no one has defaulted on their obligations….or rather there is no scope for one to default.

  36. swapnil says:

    Thank you Karthik,
    It was really very helpful.

  37. Rajesh says:

    Kathik, can u pls elaborate why the delta of the next month is higher than the delta of the near month for the same strike price?

    • Karthik Rangappa says:

      Eventually it all boils down to time. Since next month contract have lot more time to expiry, the delta is also on the higher side.

  38. Chinmay says:

    It makes sense to sell the deep otm options near expiry date as their price will definitely go down. So is it some kind very safe play? Do many people do these trades? If not, then why? Does volatility come into play?

    Sorry for so many questions but your content is really engaging. ☺

    • Karthik Rangappa says:

      It does make sense to sell deep OTM options before expiry. However, not many choose to do this because of the risk-reward ratio such strategies offer.

  39. Sarath says:

    Call option has positive delta and put option has negative delta, then how short call get negative delta…please help..

  40. chaitanya says:

    good morning karthik sir, first of all thanks a lot for such a useful modules…im just testing these strategies on NSE Paathshala…i was confused with OTM options…as tomorrow is the expiry for 29th dec CE…i took short position for 1 lot of at 8300CE at 0.65 premium…what is the profit that i receive ..assuming delta is -0.3 for short my thinking right?…if nifty goes down..then i make profit…my profit will be 75* premium at the end of the day…does people trade for such a small profits of 50-80 for a margin around 40000..

    • Karthik Rangappa says:

      Since you are short a call option, your profit is restricted to the premium you receive. In this case 0.65.

      • chaitanya says:

        okay sir…i got it.. i was going through theta.. i got the logic…here’s one more… select an option whether call or put we should check with technical analysis of underlying…to select strike price for the option we should check moneyness and delta…am i right??

  41. Ranjit kumar pandey says:

    sir from where I can find the value of delta

  42. RV4277 says:

    Nice explanation & coverage!!!!!

  43. Prithvi S Nag says:

    In the last topic i.e. Delta as a probability, you mentioned that it is favorable to sell the CE option since there is 90% probability of the option to expire OTM or worthless. the logic was the nearness of expiry date and requirement of huge movement in 2 days. My query is if the expiry date is far away, is it still recommended to sell that OTM option premium, provided the delta is currently showing value of 0.3 (arbitrary value just for understanding)?

    • Karthik Rangappa says:

      Yes, you can sell them much earlier to expiry. You can even get to keep a larger premium (provided the option expires OTM). The idea of selling near to expiry is to use time to your advantage. When you sell them before, there is a lot of time to expiry, therefore the probability of the option transitioning from OTM to ITM is higher.

      • Prithvi S Nag says:

        Thanks for the answer. Maybe we can use volatility calculations to figure out the best strike price having probability of expiring OTM or worthless? and one last query is which option premium is better to write, CE or PE?

        • Karthik Rangappa says:

          I have a preference for writing only call options. I’m a little hesitant to write Puts.

          Yes, you can (or rather should) use volatility to estimate the best strikes to write.

  44. PR7060 says:

    Sir is there any relationship between delta and intrinsic value, please explain.

  45. sandip yadav says:

    Vry nice sir


    Dear Karthika..
    If OTM options only have Extrinsic Value, and Delta only affect the Intrinsic Value, then how is Delta affect the OTM options price?

  47. sreerag says:

    Hi sir, first of all thanking you for such a wonderfull work.
    i want to ask you, like if the spot price moves up by 100 points of ABC stock and if i have an ATM call option its premium would increase by 50 points, lets say theoretically as other greeks too affect the premium pricing. But what if no any traders willing to trade when the option premium went up by 20 points, still does the option premium goes up for the next 30 points. what i exactly asking is regardless of the buying or selling pressure from the traders does the premium of the option contract goes up those 50 points?

    • Karthik Rangappa says:

      No, the premium goes up when someone trades the option. However, while trading, the smart trader would be aware of this, hence he will bid or ask at the right price point.

  48. shri31565 says:

    Dear Karthika..
    What will be the consequence, if I does not square off the position with in the market time on expiry date for the following….

    (1) Suppose I brought 9550CE at Rs.10/- and Nifty expired at 9504
    (2) Suppose I Sold 9550CE at Rs.10/- and Nifty expired at 9504

    What is my tax liability(STT) for both the case?

  49. Anshul Sharma says:

    Hey!! The articles are very nicely written. I have little doubt though, what if the combined delta is +2 for all CEs and the underlying is bearish let’s say move -200 would the option move -400?


  50. Arun says:

    Hello Karthik,
    I have few queries regarding options plz clarify.

    Call Option(Lot-100, Expiry-30th Nov)
    @10————————————————————[email protected]
    premium paid=1000 —————————– premium received=1000
    square off(sell) @15——————————- square off(buy) @5
    receive premium=1500—————————–he pay premium=500
    profit=500(1500-1000)——————————— his profit=500
    (1).is it right or wrong?
    (2).His(1st buyer) involvement closed here itself or he
    need to do anything as seller(buyer who squared off his postion)
    to buyer(2nd buyer) if the buyer hold his position until expiry?
    (3).if the buyer(who paid premium as 1000) wait until expiry if he made a profit from whom he get the money?(the seller who sold option to him already exit his position)

    TCS 2500 CE
    Spot price-2700
    If buyer wait unti expiry(until auto square off on 30th).

    On 30th few minutes before market close [email protected]

    (4).he will get 100*25=Rs2500 or something else(other payment calculation)?

    (5).In options, at any point of time the no.of Buyers= no.of Sellers or not?

    (6).How settlement is done between buyers and sellers, if at the time of expiry only 2 buyers and 2 sellers available ?

    TCS 2500 CE
    Spot price=2489
    (7).On expiry day at around 9:30am what would be the possible premium?(0.3 or 0.1 or may be greater than these values or something else).

    Plz give answers as per question numbers as i mentioned.

    Thank U.

    • Karthik Rangappa says:

      1) Yes, that right
      2) Once you square off, you are out of the market and your obligation is closed.
      3) Your profits will come from one of the sellers who made a loss. Not necessary it has to come from the same seller
      4) Upon expiry, he will get lot size * intrinsic value. The intrinsic value of a call option is either 0 or the positive difference between the strike and spot and then the put option the intrinsic value is either 0 or the positive difference between the spot and strike
      5) Not necessary. One buyer can 100 lots from 10 sellers selling 10 lots each
      6) Its cash settled by exchanges
      7) Yes, it will be quite negligible on the expiry day – I’d suspect around 1/-

      Good luck.

  51. Vikash says:

    Hi Sir,
    After reading varsity I m getting confidence to trade logically.

    Please clear my silly doubt here.

    Most of the time during expiry, premium starts erasing. If we assume that in coming last two trading days market will open flat then can we sell the call option & earn profit?
    For example – just like in Nov when nifty was at 10385ce it’s premium traded around 60-70 now the nifty at 10500ce but premium is trading at 45.) If I sell 10500ce at 45 & before expiry the premium fell to 1 0/- . So would I make 44/- pr0fit?

    • Karthik Rangappa says:

      Yes, if you think the markets are likely to stay flat, you can write the options and collect the premium. Yes, you will make 44 in profit.

  52. Vikash says:

    & merry Christmas to you.

  53. Vinod says:

    First of all thanks for such a wonderfull article/chapter. One question banknifty weekly option is expiring today and its trading @ 20 so could i sell the call option cause at the end the value would be. 05. So i would make 20 * 40/lot = 800 profit can i do this.

  54. Ashwin Revankar says:

    I’ve noticed that sometimes premium of Deep ITM or ITM option also changes in -ve. I mean if its a ITM or DITM then as per the rules the premium price should go high with respect to underlying. Right now on this date 15-06-18 if you look at HINDUNILVR option chain then you will notice that 1540 & 1580 Strike of CALL both are showing NET CHANGE -4.00 & -0.10 respectively. at the same time underlying is 1625 which is around +0.8% for the day.

    • Karthik Rangappa says:

      Yes, this is quite common and you will understand why when you read through the chapters on Volatility 🙂

  55. jayaram says:


    i want to represent the data of delta, gamma, theta in graphical form. Please help me where in this site i will get by inputting greeks data.

  56. Manas Pandey says:

    Dear sir, I have a doubt. When you say that call options have positive & puts have negative delta, isn’t this only for long calls & long puts ? Because as per what all i have understood in the previous chapter, short call should have negative delta & short put should have positive delta.

    • Karthik Rangappa says:

      You can look at it this way – the call options gain delta with an increase in price (therefore lose delta if price decreases). The put option loses delta with the increase in price (therefore increase in the delta with a decrease in price). If you have shorted a call, then you want the delta to decrease, which happens when the price drops. Likewise, if you have shorted a put, then you want the delta to decrease, which happens with the increase in price.

  57. Manas Pandey says:

    Thank you sir ?

  58. Shrey Bhandari says:


    I learned about option greek and according I took a position in Yes Bank at Spot Price:- 360 on 30Aug2018 for september expiry. I bought one Deep OTM CALL option of strike 380 @ 13.85, and also bought one Deep OTM PUT option of strike 340 @ 11.45. On 31Aug2018 Yes Bank fell 15Rs and spot price came to 345, but premium of CALL decreased by 8Rs, whereas PUT premium increased by just 1Rs. Why SO???

    As my both options were OTM and PUT option came from Deep OTM to OTM but its premium increased by just 1Rs, whereas CALL Deep OTM is still deep OTM but its premium decreased more. Please explain me?

    • Karthik Rangappa says:

      Shrey, this is a classic case of volatility driving the option premiums up. The decline in calls shows that the premiums are eroding with the drop in volatility. The put premium too on the other had and losing value, but its been offset by the drop in the spot price. Hence the calls are falling faster than that gain in puts.

  59. Ameet says:

    Can someone honestly make consecutive profit (year on year – not necessarily weekly or even monthly) if they are disciplined and with proper money management / risk management?

    Ive noticed that most teachers don’t necessarily trade their own money, but actually make money through teaching, tips, access to traders circle/group.
    With all the knowledge that one has, can you honestly say that you can make consistent profits. (40% – 60% on your capital)?
    Capital can be 1L, 10L, 1Cr or 10Cr, irrespective.

    • Karthik Rangappa says:

      That is difficult, Ameet. I’ve not been able to do that with trading. But I do know traders who have/continue to do that. I’ve had a fair bit of success with investing.

  60. priyank says:

    sir m stuck …I mean how to get delta value of any script by which formula I can get the delta value..

  61. Laksh says:

    Hi Karthik, Thanks a lot for another insightful article. It really helps a lot.

    Quick question- I bought a Nifty Put option at Rs. 9 today; Delta 0.14. Nifty gained 60 points from there. Going by the standard Delta calculation, the premium should have dropped to Rs. 4.5 approx. While in reality, it came down to Rs. 7 only.

    What do think I am missing here?

    Thanks, Laksh

  62. Ananth Gopal says:

    Hello Karthik,

    I have few queries in regards to Bank Nifty for the week 15th Nov 2018. Please find the link below.

    The strike prices that I am talking about are
    1. Bank Nifty15th Nov 26100 PE
    2. Bank Nifty 15th Nov 26100 CE
    3. Bank Nifty 15th Nov 26000 CE
    On 15th Nov, Bank nifty closed at 26154.75. Considering 15th Nov as the expiry day of that week, the value of the PUT option strike has come down to 0.05, however the value of the Call option both 26100 and 26000 hasn’t come down and also at the end of closing hours of trading I could see traders buying and selling the Call option strikes. I would like to know as to why the value of Call option did not reduce and why the traders were trading the strike price even at the close hours and what would have happened after closing hours of market to these Call options and how would it have affected the traders who bought or sold at the last minute.

    • Karthik Rangappa says:

      Ananth, both 26000 and 26100 CE has intrinsic values of 154.75 and 54.75, so it cannot come down to 0. The reason why traders were transaction was to probably close the postions.

  63. Ananth Gopal says:

    Hello Karthik,

    I am trying to post a link from google drive and queries in regards to the same, however it is not getting posted. I am not sure what I am missing. Please help.
    Thanks in advance.

  64. Ananth Gopal says:

    Hello Karthik,

    I have few queries in regards to Bank Nifty for the week 15th Nov 2018. Please find the link below.

    The strike prices that I am talking about are
    1. Bank Nifty15th Nov 26100 PE
    2. Bank Nifty 15th Nov 26100 CE
    3. Bank Nifty 15th Nov 26000 CE
    On 15th Nov, Bank nifty closed at 26154.75. The value of the PUT option strike has come down to 0.05, however the value of the Call option both 26100 and 26000 hasn’t come down and also at the end of closing hours of trading I could see traders buying and selling the Call option strikes. I would like to know as to why the value of Call option did not reduce and why the traders were trading the strike price even at the close hours and what would have happened after closing hours of market to these Call options and how would it have affected the traders who bought or sold at the last minute.

  65. Ananth Gopal says:

    Hello Karthik,

    I have few queries in regards to Bank Nifty for the week 15th Nov 2018.
    The strike prices that I am talking about are
    1. Bank Nifty15th Nov 26100 PE
    2. Bank Nifty 15th Nov 26100 CE
    3. Bank Nifty 15th Nov 26000 CE
    On 15th Nov, Bank nifty closed at 26154.75. On the expiry day the value of the PUT option strike (ATM) came down to 0.05, however the value of the Call option (ATM) 26100 closed at 43.20 and call option 26000 (Slightly ITM) closed at 133.30. I could see traders buying and selling the Call option strikes at the last minute of trading hours. I would like to know as to why the value of Call option did not reduce and why the traders were trading the strike price even at the close hours and what would have happened after closing hours of market to these Call options and how would it have affected the traders who bought or sold at the last minute.

    I wanted to show you the image that I captured for the same, however I am not able add the link in here.

  66. Srikrishna Rowthu says:

    Hi Zerodha,

    Firstly, I feel a sense of confidence over my fundamental knowledge while I go through varsity. It’s really easy to understand. For that I wanna appreciate you and your team efforts personally. Grateful to your efforts.
    Coming to the topic. I have a doubt in this module.
    Look at the below line in double quotes.
    “Likewise if you short a PUT option the delta turns positive. -1 * (-0.5) = +0.5”

    Generally if we short a PUT option, we collect the premium instantly and any increase in the premium won’t add more money to the position. If my understanding is right, why are we even calculating delta in that case?

    Can you please elaborate here. Thanks in advance:)


    • Karthik Rangappa says:

      Thanks for the kind words, Srikrishna.
      Delta, like other option greeks is a sensitivity of the option premium, which need to understand when assuming any position in the option market. Yes, increase in premium does not add more money, but it does have an impact on your P&L, right? This is a risk and should be measured by its sensitivity.

      • Srikrishna Rowthu says:

        This is my understanding after reading your comments.

        If I am in loss while selling put option at a particular point of time. And later, there is an increase of 1 point in the underlying. Now, accordingly we have an increase of (-1 * (-0.5) = +0.5) 0.5 for the option. So, there is an effect on P&L here.

        But, if I am in profit while selling put option again at a particular instant of time and later there is an increase of 1 point in the underlying. Now, the above calculation of 0.5 is not valid in this case. Since, we have already collected the premium and more increase from here won’t be adding to our position(P&L).

        Is my understanding correct? Please let me know.

  67. Srikrishna Rowthu says:

    Hi Karthik,

    Can you please explain me how the probability of the option expiring in ITM is determined?


    • Karthik Rangappa says:

      The delta of the option kind of conveys the probability of the option expiring ITM. For example, if the delta is 0.2, then there is a 20% for this option to transition from OTM to ITM. So on and so forth.

      • Srikrishna Rowthu says:


        I actually wanna know the calculation behind this –
        “If the delta is 0.2, then there is a 20% probability for the option to transition from OTM to ITM”.

        I want to know how the relationship between the delta and the above probability is determined?
        And also I have asked one more doubt just above this question. Can you please answer that as well? Thanks in advance.


        • Karthik Rangappa says:

          This is just a proxy (a very good one though), Srikrishna. I dint get the other question, can you please ask that again? Thanks.

  68. ujwal says:

    sir, i am completing MBA in FINANCE , I want to ask about NISM-MOODY CDMS cource it is good 4 me to do.because i am searching job in derivative section.please help me out.

  69. PANKAJ says:

    A Terminal which show all Greek like
    gama delta theta Vega rho value at time
    also provide good candle chart
    PPlease tell me the name of such Terminal How can I purchase them
    Can zerodha provide such terminal which enriches in all fundamentals Technical value chart and cover also Greek value in one singht

  70. PANKAJ says:

    in kite .zerodha. com
    exactly where Greek delta theta Vega
    value can see
    means which heading is locate
    Please guide

  71. Hemant Kumar says:

    Is there any penalty imposed by exchange after shorting call or put options if i don’t buy it back before expiry?

    suppose 24 july, 2019 i take a short position in Infosys for call option and expiry date is 26 july, 2019. If i don’t buy it back before 26 july then what are it’s implications ?

  72. Kunal says:

    Dear Karthik,

    I have recently started studying the greeks and request you to please clear a doubt. In case 2, where the trader has both call and put options and the total delta is coming to 0.25, im just wondering what is his thought process behind buying various call options? i was wondering if he wanted a delta of 0.25, he could have as well bought 5 ATM call options.
    thanks in advance 🙂

    • Karthik Rangappa says:

      Kunal, 5 ATM will make it 2.5 delta, which is very different from 0.25 Delta. At 0.25 delta, you are neutral about the markets, but at 2.5 delta, you are bullish.

  73. Amol says:

    Dear karthik,
    suppose spot is 11000(Nifty), if i sell call(ATM) & put(ATM) at 11000 strike, overall delta will be neutral? but how overall delta will behave if spot moves up & down? let us take consider stock will move up +400 points & then it will go down by -400.

    would u please explain how delta changes when we short the options ? i am asking question because in Delta part 3 chapter, less examples are given as to how delta changes for sell options.

    • Karthik Rangappa says:

      You are right, the delta changes with the spot and this change the delta position. For you to maintain a delta neutral position, you will have to ensure you rebalance and add more legs to your position. This can be an expensive affair.

  74. Amol says:

    Hello karthik,
    thanks for ur reply. Right now banknifty is hovering around 27860, if i sell call at 358 & sell put at 282 with 27800 strike, would u plz tell me after which point on either side( up & down) i will start to loose money. Expiry of these option is 29 aug 19. but i do not want P&L on expiry day as i know that. i want to know P&L before expiry.

    • Karthik Rangappa says:

      The sum of premiums is 358+282 = 648.

      You’ll lose money if Banknifty moves above (strike + sum of premiums) 28448 or below (strike – the sum of premiums) 27152.

  75. Amol says:

    Hi karthik, where can i get current volatility of bank nifty ?

  76. Vikas says:

    If call option is bought Deep OTM and market goes up and delta reaches to OTM or ATM and premium increased as well then :
    1) can we book profit by selling at ATM or OTM ?. ( as we are selling at high premium and buying at low premium although the IV is 0 or spot price does not cross strike price).

  77. Prasanna says:

    Hi Karthick,

    Great article I have been going through your lessons and they are the most easy to understand for a layman like me who doesnt have any prior knowledge about markets.

    By the way I didn’t understand the last point in the lecture about probability of the option expiring in ITM and writing the option can you please elaborate it.

    • Karthik Rangappa says:

      Thanks, Prasanna. The delta can also be looked up as a probabilistic indicator, which tells you the probability of the option closing ITM. For example, an option with delta of 0.4 indicates that the option has only 40% chance of expiring ITM. An option with 0.8 delta indicates that it has 80% chance of expiring ITM.

Post a comment