Module 5   Options Theory for Professional TradingChapter 9

The Option Greeks (Delta) Part 1

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9.1 – Overview

Yesterday I watched the latest bollywood flick ‘Piku’. Quite nice I must say. After watching the movie I was casually pondering over what really made me like Piku – was it the overall storyline, or Amitabh Bachchan’s brilliant acting, or Deepika Padukone’s charming screen presence, or Shoojit Sircar’s brilliant direction? Well, I suppose it was a mix of all these factors that made the movie enjoyable.

This also made me realize, there is a remarkable similarity between a bollywood movie and an options trade. Similar to a bollywood movie, for an options trade to be successful in the market there are several forces which need to work in the option trader’s favor. These forces are collectively called ‘The Option Greeks’. These forces influence an option contract in real time, affecting the premium to either increase or decrease on a minute by minute basis. To make matters complicated, these forces not only influence the premiums directly but also influence each another.

To put this in perspective think about these two bollywood actors – Aamir Khan and Salman Khan. Movie buffs would recognize them as two independent acting forces (similar to option Greeks) of Bollywood. They can independently influence the outcome of the movie they act in (think of the movie as an options premium). However if you put both these guys in a single flick, chances are that they will try to pull one another down while at the same time push themselves up and at the same time try to make the movie a success. Do you see the juggling around here? This may not be a perfect analogy, but I hope it gives you a sense of what I’m trying to convey.

Options Premiums, options Greeks, and the natural demand supply situation of the markets influence each other. Though all these factors work as independent agents, yet they are all intervened with one another. The final outcome of this mixture can be assessed in the option’s premium. For an options trader, assessing the variation in premium is most important. He needs to develop a sense for how these factors play out before setting up an option trade.

M5-Ch9-Illustration1 So without much ado, let me introduce the Greeks to you –

  1. Delta – Measures the rate of change of options premium based on the directional movement of the underlying
  2. Gamma – Rate of change of delta itself
  3. Vega – Rate of change of premium based on change in volatility
  4. Theta – Measures the impact on premium based on time left for expiry

We will discuss these Greeks over the next few chapters. The focus of this chapter is to understand the Delta.

9.2 – Delta of an Option

Notice the following two snapshots here – they belong to Nifty’s 8250 CE option. The first snapshot was taken at 09:18 AM when Nifty spot was at 8292.

Image 1_at 918
A little while later…

Image 2_nifty 8316

Now notice the change in premium – at 09:18 AM when Nifty was at 8292 the call option was trading at 144, however at 10:00 AM Nifty moved to 8315 and the same call option was trading at 150.

In fact here is another snapshot at 10:55 AM – Nifty declined to 8288 and so did the option premium (declined to 133).

Image 3_nifty 8288

From the above observations one thing stands out very clear – as and when the value of the spot changes, so does the option premium. More precisely as we already know – the call option premium increases with the increase in the spot value and vice versa.

Keeping this in perspective, imagine this – you have predicted that Nifty will reach 8355 by 3:00 PM today. From the snapshots above we know that the premium will certainly change – but by how much? What is the likely value of the 8250 CE premium if Nifty reaches 8355?

Well, this is exactly where the ‘Delta of an Option’ comes handy. The Delta measures how an options value changes with respect to the change in the underlying. In simpler terms, the Delta of an option helps us answer questions of this sort – “By how many points will the option premium change for every 1 point change in the underlying?”

Therefore the Option Greek’s ‘Delta’ captures the effect of the directional movement of the market on the Option’s premium.


The delta is a number which varies –

  1. Between 0 and 1 for a call option, some traders prefer to use the 0 to 100 scale. So the delta value of 0.55 on 0 to 1 scale is equivalent to 55 on the 0 to 100 scale.
  2. Between -1 and 0 (-100 to 0) for a put option. So the delta value of -0.4 on the -1 to 0 scale is equivalent to -40 on the -100 to 0 scale
  3. We will soon understand why the put option’s delta has a negative value associated with it

At this stage I want to give you an orientation of how this chapter will shape up, please do keep this at the back of your mind as I believe it will help you join the dots better –

  1. We will understand how we can use the Delta value for Call Options
  2. A quick note on how the Delta values are arrived at
  3. Understand how we can use the Delta value for Put Options
  4. Delta Characteristics – Delta vs. Spot, Delta Acceleration (continued in next chapter)
  5. Option positions in terms of Delta (continued in next chapter)

So let’s hit the road!

9.3 – Delta for a Call Option

We know the delta is a number that ranges between 0 and 1. Assume a call option has a delta of 0.3 or 30 – what does this mean?

Well, as we know the delta measures the rate of change of premium for every unit change in the underlying. So a delta of 0.3 indicates that for every 1 point change in the underlying, the premium is likely change by 0.3 units, or for every 100 point change in the underlying the premium is likely to change by 30 points.

The following example should help you understand this better –

Nifty @ 10:55 AM is at 8288

Option Strike = 8250 Call Option

Premium = 133

Delta of the option = + 0.55

Nifty @ 3:15 PM is expected to reach 8310

What is the likely option premium value at 3:15 PM?

Well, this is fairly easy to calculate. We know the Delta of the option is 0.55, which means for every 1 point change in the underlying the premium is expected to change by 0.55 points.

We are expecting the underlying to change by 22 points (8310 – 8288), hence the premium is supposed to increase by

= 22*0.55

= 12.1

Therefore the new option premium is expected to trade around 145.1 (133+12.1)

Which is the sum of old premium + expected change in premium

Let us pick another case – what if one anticipates a drop in Nifty? What will happen to the premium? Let us figure that out –

Nifty @ 10:55 AM is at 8288

Option Strike = 8250 Call Option

Premium = 133

Delta of the option = 0.55

Nifty @ 3:15 PM is expected to reach 8200

What is the likely premium value at 3:15 PM?

We are expecting Nifty to decline by – 88 points (8200 – 8288), hence the change in premium will be –

= – 88 * 0.55

= – 48.4

Therefore the premium is expected to trade around

= 133 – 48.4

= 84.6 (new premium value)

As you can see from the above two examples, the delta helps us evaluate the premium value based on the directional move in the underlying. This is extremely useful information to have while trading options. For example assume you expect a massive 100 point up move on Nifty, and based on this expectation you decide to buy an option. There are two Call options and you need to decide which one to buy.

Call Option 1 has a delta of 0.05

Call Option 2 has a delta of 0.2

Now the question is, which option will you buy?

Let us do some math to answer this –

Change in underlying = 100 points

Call option 1 Delta = 0.05

Change in premium for call option 1 = 100 * 0.05

= 5

Call option 2 Delta = 0.2

Change in premium for call option 2 = 100 * 0.2

= 20

As you can see the same 100 point move in the underlying has different effects on different options. In this case clearly the trader would be better off buying Call Option 2. This should give you a hint – the delta helps you select the right option strike to trade. But of course there are more dimensions to this, which we will explore soon.

At this stage let me post a very important question – Why is the delta value for a call option bound by 0 and 1? Why can’t the call option’s delta go beyond 0 and 1?

To help understand this, let us look at 2 scenarios wherein I will purposely keep the delta value above 1 and below 0.

Scenario 1: Delta greater than 1 for a call option

Nifty @ 10:55 AM at 8268

Option Strike = 8250 Call Option

Premium = 133

Delta of the option = 1.5 (purposely keeping it above 1)

Nifty @ 3:15 PM is expected to reach 8310

What is the likely premium value at 3:15 PM?

Change in Nifty = 42 points

Therefore the change in premium (considering the delta is 1.5)

= 1.5*42

= 63

Do you notice that? The answer suggests that for a 42 point change in the underlying, the value of premium is increasing by 63 points! In other words, the option is gaining more value than the underlying itself. Remember the option is a derivative contract, it derives its value from its respective underlying, hence it can never move faster than the underlying.

If the delta is 1 (which is the maximum delta value) it signifies that the option is moving in line with the underlying which is acceptable, but a value higher than 1 does not make sense.  For this reason the delta of an option is fixed to a maximum value of 1 or 100.

Let us extend the same logic to figure out why the delta of a call option is lower bound to 0.

Scenario 2: Delta lesser than 0 for a call option

Nifty @ 10:55 AM at 8288

Option Strike = 8300 Call Option

Premium = 9

Delta of the option = – 0.2 (have purposely changed the value to below 0, hence negative delta)

Nifty @ 3:15 PM is expected to reach 8200

What is the likely premium value at 3:15 PM?

Change in Nifty = 88 points (8288 -8200)

Therefore the change in premium (considering the delta is -0.2)

= -0.2*88

= -17.6

For a moment we will assume this is true, therefore new premium will be

= -17.6 + 9

= – 8.6

As you can see in this case, when the delta of a call option goes below 0, there is a possibility for the premium to go below 0, which is impossible. At this point do recollect the premium irrespective of a call or put can never be negative. Hence for this reason, the delta of a call option is lower bound to zero.

9.4 – Who decides the value of the Delta?

The value of the delta is one of the many outputs from the Black & Scholes option pricing formula. As I have mentioned earlier in this module, the B&S formula takes in a bunch of inputs and gives out a few key outputs. The output includes the option’s delta value and other Greeks. After discussing all the Greeks, we will also go through the B&S formula to strengthen our understanding on options. However for now, you need to be aware that the delta and other Greeks are market driven values and are computed by the B&S formula.

However here is a table which will help you identify the approximate delta value for a given option –

Option Type Approx Delta value (CE) Approx Delta value (PE)
Deep ITM Between + 0.8 to + 1 Between – 0.8 to – 1
Slightly ITM Between + 0.6 to + 1 Between – 0.6 to – 1
ATM Between + 0.45 to + 0.55 Between – 0.45 to – 0.55
Slightly OTM Between + 0.45 to + 0.3 Between – 0.45 to -0.3
Deep OTM Between + 0.3 to + 0 Between – 0.3 to – 0

Of course you can always find out the exact delta of an option by using a B&S option pricing calculator.

9.5 – Delta for a Put Option

Do recollect the Delta of a Put Option ranges from -1 to 0. The negative sign is just to illustrate the fact that when the underlying gains in value, the value of premium goes down. Keeping this in mind, consider the following details –

Parameters Values
Underlying Nifty
Strike 8300
Spot value 8268
Premium 128
Delta -0.55
Expected Nifty Value (Case 1) 8310
Expected Nifty Value (Case 2) 8230

Note – 8268 is a slightly ITM option, hence the delta is around -0.55 (as indicated from the table above).

The objective is to evaluate the new premium value considering the delta value to be -0.55. Do pay attention to the calculations made below.

Case 1: Nifty is expected to move to 8310

Expected change = 8310 – 8268

= 42

Delta = – 0.55

= -0.55*42

= -23.1

Current Premium = 128

New Premium = 128 -23.1

= 104.9

Here I’m subtracting the value of delta since I know that the value of a Put option declines when the underlying value increases.

Case 2: Nifty is expected to move to 8230

Expected change = 8268 – 8230

= 38

Delta = – 0.55

= -0.55*38

= -20.9

Current Premium = 128

New Premium = 128 + 20.9

= 148.9

Here I’m adding the value of delta since I know that the value of a Put option gains when the underlying value decreases.

I hope with the above two Illustrations you are now clear on how to use the Put Option’s delta value to evaluate the new premium value. Also, I will take the liberty to skip explaining why the Put Option’s delta is bound between -1 and 0.

In fact I would encourage the readers to apply the same logic we used while understanding why the call option’s delta is bound between 0 and 1, to understand why Put option’s delta is bound between -1 and 0.

In the next chapter we will dig deeper into Delta and understand some of its characteristics.

Key takeaways from this chapter

  1. Option Greeks are forces that influence the premium of an option
  2. Delta is an Option Greek that captures the effect of the direction of the market
  3. Call option delta varies between 0 and 1, some traders prefer to use 0 to 100.
  4. Put option delta varies between -1 and 0 (-100 to 0)
  5. The negative delta value for a Put Option indicates that the option premium and underlying value moves in the opposite direction
  6. ATM options have a delta of 0.5
  7. ITM option have a delta of close to 1
  8. OTM options have a delta of close to 0.


  1. khyati verdhan says:

    Hi kartik,
    Very very thanks for new chapter. Contents are very good and clear but incomplete knowledge create confusion. So, I am waiting with Patience for your completing this module.

    • Karthik Rangappa says:

      Thanks for you patience, we are working on the new chapter…will put up up as soon as we can.

      • jyotsana says:

        hey Nikhil ,i have learnt alot from zerodha varsity. While going through this chapter and solving examples a doubt would be great if you could look into it.

        In the example of call option where you talk about the role delta plays when one expects nifty to drop and the example where you take delta below 0. in these two case there is certain differences in computation of premium. i believe as per the computation in first example ,in later example it should have been

        change in nifty= 8200-8288= -88
        expected change in premium =
        -88*(-0.2) = 17.6
        hence new premium shall be 9+17.6=26.6

        please look into it.and let me know if i have misunderstood the concept

        • Karthik Rangappa says:

          Glad to note that, Jyotsana. By the way, the way to determine the change in Delta is by calculating the change in Nifty points multiplied by the Delta….so in this case –

          88*0.2 = 17.6.

          If you are long Call, add the delta to the premium, if you are short call, deduct the delta from the premium. Do not consider the algebraic sign at the time of calculating the change in delta. Easier this way 🙂

    • Harish says:

      BS has been known to be erroneous for NIFTY (Asian Journal for Management) , how does one trust the Greeks then ? Is there a modification in BS Formula to consider the NIFTY.

      • Karthik Rangappa says:

        Well, in that case, no model is perfect 🙂 I’m not sure if there is a variant which fits Nifty well. I need to check this.

  2. Pravin says:

    Thank you very much for explaining the difficult subject in easy way. It’s really appreciable & thank you once again for taking so much pain to explain rather complicated things.
    Keep it up. Awaiting eagerly for next chapters.

  3. rahul says:

    waiting for next chapter …..

  4. aditya garg says:

    hey first of all thanks for explaining the delta in such a simple way.
    when will be the chapter on option strategies will come?

    • Karthik Rangappa says:

      The module on Option stratergies will take some time…we will start work on that once the ongoing module on Options Theory is through.

  5. SUBHANKAR says:

    If i sell first a stock at 25 and then buy at 20 before expiry , then my profit is 5 plus premium received. Am i right?

    • Karthik Rangappa says:

      Let me rephrase this – If you sell an option (not stock) at a premium of 25 and buy the option back at 20, then the profit you make is Rs.5/- times the lot size”.

      • SUBHANKAR says:

        why not premium received?

        • Karthik Rangappa says:

          Can you please elaborate your query, I’m unable to understand the context. Thanks.

        • hkr72 says:

          You may have already realized answer to your question. If not, you received Rs25/- premium for selling the call option, which is already considered in the calculation, right ?

          profit=(25-20)*lot size —- assuming you bought same number of contracts (lots), which you should be doing.

  6. Ragunathan says:

    Hi Karthik
    Your contents are very lucid that a layman in the Dalal Street can know more about the options trading.
    This chapter particularly

    //the option is gaining more value than the underlying itself. Remember the option is a derivative contract, it derives its value from its respective underlying, hence it can never move faster than the underlying. If the delta is 1 (which is the maximum delta value) it signifies that the option is moving in line with the underlying which is acceptable, but a value higher than 1 does not make sense. For this reason the delta of an option is fixed to a maximum value of 1 or 100.//

    its a fantastic explanation about the delta value. Thanks for the contents. Need More classes like this.

    • Karthik Rangappa says:

      Thanks for the kind words and encouragement 🙂

      We are working towards putting up the chapters soon. Should be out soon.

  7. NARSIMHA says:

    sir,(personnel)with all my experience&sufferings i strongly beleive technicals,charts,indicators,etc wont work in options trading,it purely depends on greeks&mass psycycology&what u advised in t.analysis ie best suited for equities&fut moreover i didnt got any justification correct me if iam wrong&i wantededucational moves in TRADING

    • Karthik Rangappa says:

      You are absolutely right – when it comes to option trading you should be using Option Greeks and other parameters to trade and not really Technical Analysis.

    • NARSIMHA says:

      sir,thanks again(pnl) iam running a small business(mall) problem is iam unable to adjust money for trading,whatever comes by sales,borrowings will not be sufficieent for retail busin,iam unable to trade frely&give time to loss&repair in that pressure i end up loosing even i know many thiings which i learnt at somecost&3yrs now i dont want to waste my experience&knowledge&loose my passion which may turn to fortune in future if iam right so whats way,advise.

      • Karthik Rangappa says:

        Take it easy is the advice 🙂 Here is what I would suggest –

        1) Concentrate on your core business and try to improvise on the same

        2) Do not trade the markets if you feel you are getting too stressed and therefore making losses

        3) Slowly unlearn everything about the markets you know so far and then try to relearn in a structured way

        4) Start with small amounts of investments (no trading)

        5) Invest small amounts and watch it grow

        6) Once you are comfortable with that, try investing significant amounts with an intention of creating wealth

        7) And if you have gained enough confidence by then maybe you can dabble with small amounts of restricted trading

        If you follow this, I have a feeling you will be in a much better position in the future.

        • NARSIMHA says:

          sir,thanks,i dont think investing works in these econimic conditions as middleclass i cant about my core business my wife will always looks iam only a supporter with all this network i want something on my own,thatswhy iam passioate for this business for timebeing iam planning to trde 8 lots nifty options&1 fut stock as ur t.analysis teached sorry iam working smartly to overcome&win

        • Manish says:

          Hi, just a question though it’s out of context but haven’t got this answer from anybody. When one sells a call option that means he has created a short position so can he close his position whenever he feels like or it will only close when the buyer of the call closes it. Have you in any of your chapters explained this. Not able to understand when analysts say that the price is above strike price nd now we can see shortcovering

          • Karthik Rangappa says:

            You can close the short position anytime you want, not need to wait for either expiry or for the counterparty to close the position. This is true with long options as well.

      • NARSIMHA says:

        sir,in morning trade first 2 min,why cant we trade (open=low)for long (open=high)for short,ithink it is marubuzo can we trade for v short time within 10min

  8. khyati verdhan says:

    Hi kartik,
    I am an intra day trader. So, I never wait expiry to collect premium. So my question is — suppose nifty CE with strike price of 8200 and premium of 120 and delta or 5.5. If I were execute an long or short order and price moves some favour in my direction then my profit is equal on long or short position and risk should also be same on long and short orders depending upon the points I trail on stop loss on either side. The only difference is that I have to deposit margin money on short orders. Am I correct??? Please clarify.

    • Karthik Rangappa says:

      When you say delta is 5.5 I hope you are talking about the 0 to 100 scale.

      P&L on options is non linear. So when you buy a call option the profit you enjoy is very different from the profits you would enjoy when you are short. Likewise for risk.

      Yes, when you short the margins are blocked from you trading account.

  9. Ragunathan says:

    Where can we know the Greeks value for Nifty options?

  10. R SRINIVASAN says:

    How does the value of Delta change with time decay?
    Where we can get the delta values?

    • Karthik Rangappa says:

      You can get the delta value from the Options calculator. Will discuss Delta against time shortly.

  11. Sumit says:

    Hi Karthik,

    One thing I am not able to understand since long is, how derivative follows underlying stock/index price and that too in very much sync? As per my understanding option price is decided by last trade price transaction(LTP) of that option. Then following somehting should not be practically possible. Lets say for example, If nifty is going down and suddenly some people try to buy options in extremely large quantity then that option price should increase but it does not happen. I have observed there is no relation of volume in price of options. if option price is calculated based on delta, theta, vega, time decay etc then who decides it? is someone punches that into system or exchange computers calculate based on these greeks formula and display as LTP? or is it just simple last trade price?


    • Karthik Rangappa says:

      A derivative by definition is a contract that derives its value based on an underlying. Hence technically speaking derivatives cannot influence the spot. Option price is not decided by LTP, in fact LTP is decided by Option Pricing which in turn is depended on the Option Greeks. Volume is a function of pure demand and supply…so that is a different perspective all together.

      • Vetriselvan says:

        Hi Karthick,

        I had the same question. Just to clarify myself, I have two more questions.

        1. So, can we say that volumes in the options does not influence option prices?.
        2. It should be the exchange that enforces the prices and not the participants in the options market right?

        Thank you for your time.

        • Karthik Rangappa says:

          1) No, not really. There are more influencing factors than Volume.
          2) No, options is tradable, hence the market decides the rate. The Exchange does not have a role to play in option pricing.

          • Sidharth says:

            HI Karthik

            Can you please elaborate on why no, since your answer is open ended.

            1. Say if “Call” Option x currently trading at 100 and underlying assest trading at 1000.

            we have 10 lots of sell order at 105, 10 at 110, 20 at 120. Total 40 sell orders at different prices. No buy orders as of now.

            Later some point one buyer ordered 40 buy order at market price, same time underlying asset price droping to 980. But no new sellers of option.

            In this case, after executing all 40 orders, LTP is 120 right….

          • Karthik Rangappa says:

            Yes, 120 would be the last traded price.

  12. kieron says:

    Nifty @ 10:55 AM is at 8268

    Option Strike = 8250 Call Option

    Premium = 133

    Delta of the option = 0.55

    In above example how you take or calculate premium value 133 and delta option value 0.55

    • Karthik Rangappa says:

      This was just an illustration – also do notice I have mentioned spot @ 8268 and strike @ 8250, hence this is an ITM option … therefore the Delta should be more than 0.5 – hence the assumption that the delta is 0.55.

  13. Mamata nayak says:

    Where can one get delta value of nifty options on a real time basis ?

  14. jagadeesh says:

    Awesome…. Thank you so much for your untiring effort sir…

  15. Ragunathan says:

    When will you post the next part. We are waiting…

  16. NARSIMHA says:

    sir,for eod trades there is good website called TOP STOCK RESEACH IF U R FREE CHECK&ADVISE

  17. Debasish Panigrahi says:

    Hi Karthik,

    It’s a really nice write up.I have some queries.

    Say NIFTY is trading at 8300 and there are still 10 days to expiry.Assume NIFTY 8400CE is trading at 30. Suddenly NIFTY spikes by 50 points and 8400CE suddenly becomes 50 +. Why the demand-supply equation doesn’t govern the option price ?Is it like sellers drop suddenly or buyers increase instantly ?Even if the option greeks control premium pricing,shouldn’t buy/sell numbers decide the price ? Sometimes the nifty spot price moves by 10 points (+ve), nearest CE moves by 2 rs sometimes and sometimes 5 rs. So what should be the definitive way to calculate ?


    • Karthik Rangappa says:

      You answered it yourself – this about it bit by bit –

      1) What is demand supply situation in the market?

      Ans – It is the pressure to buy or sell a particular asset

      2) What happens when the pressure builds?

      Ans – Depending on the strength of the pressure (either there is more selling pressure of more buying pressure) the market moves in a certain direction.

      3) What happens to options when the market moves?

      Ans – The premium changes

      4) By how much does the premium change?

      Ans – That depends on the delta!

      So as you see – Delta is captures the effect of directional movement, which by itself is a function of demand and supply of the market.

      • Debasish Panigrahi says:

        Thanks a lot for the reply Karthik. So, can we directly bet on the delta then via some instrument which is like “derivative of a derivative” ?

  18. Pankit Shah says:

    Dear kartik,
    I have understood call & put options,but i m confused regarding trading with put on the trading terminal.
    Lets say i buy nifty put 8150 @ 100.After 3 days the nifty spot is at 8000 and premium @ 110…so how do i profit from above trade…if i sell put 8150..i would make a loss of 110-100=10*25=250…am i right sir?

    • Karthik Rangappa says:

      Let me just rephrase what you’ve said –

      Option Type – Nifty Put
      Strike – 8150
      Premium Paid – 100
      Trade type – Long Put (buy put option)

      3 days later…

      Nifty Spot – 8000
      Premium – 110
      Profit = 110 -100 = Rs.10/=

      Total Profit = 10 * 25 = Rs.250/-

      So you make a profit on this trade and not a loss 🙂
      Premium – 110

      • Saurabh Garg says:

        Sir, my question is related to the above example only. When we bought a put at 8150 and now the spot price is 8000 then isn’t the profit 8150-8000= 150
        & 150-100(premium paid)= 50*25=1250

        Because in previous examples, u calculated profit with the difference in the value of underlying asset instead of the value of premium.

        • Karthik Rangappa says:

          Saurabh – yes, the profit will be at least to the extent of the intrinsic value..which in this case happens to be 8150 minus 8000 = 150. However I dint want to say this as I was worried about creating confusion. Hence used the same numbers Pankit quoted 🙂

          • Hari says:

            Hi Karthik bro,

            Now I am confused..shouldn’t SAURABH GARG calculation only be used when exercising the option and not when “trading” premium i.e. not waiting for expiry?

            Thanks bro 🙂

          • Karthik Rangappa says:

            Yes, the Option P&L before the expiry will be lot different when compared to the P&L on expiry. The calculation here is for expiry.

  19. Insomniac Trader says:

    Dear Karthik Rangappa,

    You deserve praise and thanks for taking all the troubles to
    write it all quite clearly and making it all easily

    You do not have to publish the rest of this post: I just
    thought I will bring 2 minor items (nit-picking, really!) to
    your attention.

    Section 9.2 : “Delta of an Option” : 2nd sentence:

    “The first snapshot was taken at 09:18 AM when Nifty spot
    was trading at 8278 (not captured in the snapshot). ”

    1. The parenthetical remark “not captured in the snapshot” is
    not quite correct:

    In fact, Nifty is right there: see the line immediately below
    “VWAP” on the “Fundamentals” tab:

    Underlying Value : 8292.65

    2. Nifty is an Index: it is not a traded asset.

    So, the second part of the the sentence

    “when Nifty spot was trading at 8278 ….”

    can be stated more simply as :

    “when Nifty was at 8278…”

    (if one wants to be very pedantic and precise!)

    If you agree on this change, you will have to make similar
    changes at quite a few other places as well.

    A good teacher sometimes deliberately makes mistakes in the class to
    find out if the audience is alert or sleeping! Perhaps you too
    inserted such mistakes to test if your audience is alert!

    With best regards,

    J. Viswanathan.

    • Karthik Rangappa says:

      Wow! Thank you so much for pointing out these errors. I have made the necessary changes. The errors are not intentional and attributable to oversight. I would be very grateful if you can help in pointing out these errors. Please feel free to email these errors to me at karthik.r at zerodha dot com.

  20. iyengarnsv says:

    We are expecting the underlying to change by 42 points (8310 – 8288), hence the premium is supposed to increase by

    = 22*0.55

    Sir above 42 should be 22

  21. iyengarnsv says:

    Delta of the option = 1.55 (purposely keeping it above 1)
    Sir this should be 1.5 (Please see 1.5*42=63)

  22. iyengarnsv says:

    Change in Nifty = 68 points (8288 -8200)
    Instead of 68 points it should be 88

  23. richa bohra says:

    I know that if i am making loss as a buyer of an option i can simply allow my option to expire. and if i am making loss i will have to forgo the margin. But what if

    A. As buyer of a call or put option i am making profit on the expiry but i don’t exercise the option. will i get the profit or not.
    B. If i sold a call or put option and i am making profit on the expiry day but do not square off my position on the expiry.

    Thanks and regards

    • Karthik Rangappa says:

      When you buy an option you pay the full premium required and not really margins. You pay margins when you short option.

      1) When you buy options and hold it till expiry then on the expiry day whatever profits you are entitled will be credited to your trading account.
      2) When you short options and hold it till expiry then on the expiry day whatever profits you are entitled will be credited to your trading account. However STT on short option positions is quite high, so its advisable to close the trade yourself and not hold till expiry.

      • Srinathjayanna says:

        1 sir isn’t the stt same for buying and selling 0.05% on premium value and 0.125% on excersized contract value.
        2.And if we are short on options we will be paying the stt at selling side only and why we need to worry about stt on buying side.
        3.stt is high only on long positions itm options right.

        • Karthik Rangappa says:

          1) Yes, the ‘value’ and how it is calculated varies based on the moneyness of the option, and hence such a big impact
          2) Look at it in terms of moneyness
          3) Yes

  24. Harshendra Singh says:

    Many articles including wikipedia
    ( describe five Greeks,the last being RHO which is not described here. Why is it so ?

    • Karthik Rangappa says:

      Rho is mainly with respect to Rate of change of underlying with changes in the interest rate. For all practical purpose the change in interest rate is minimal, and that makes Rho not a very active Greek…so I’m still contemplating to include this or not 🙂

  25. sarath says:

    is there is any option to calculate current delta of an option ?

  26. Vasanth says:

    As mentioned in the above comments, while trading options it is advised to use Greeks and other parameters not really TA. My doubt is that after TA only we can predict the direction and position according to the view. Option Greek will increase the success probability but TA will be the base.. Correct me if am wrong.

  27. Vasanth says:

    Can you highlight the other parameters to be considered apart from Greeks while trading options?

  28. uday says:

    Please give me link on NSE for these greeks.regards

  29. ShreyaDR says:

    where to get values of Option Greeks before trading in options

  30. B S SRIHARSHA says:

    Do you have a strategy for getting monthly income through Nifty options,keeping in mind the market tank on 24Aug2015, are there any option strategy that will protect ones capital

  31. Sir,
    I have a doubt. For example, if i sell a lot at X premium price and waited till the expire day. I think the value of premium will approaches 0 (or say some lesser value) at the time if i bought a lot. Then i may get profit of X/lot. Is it possible??

    • Karthik Rangappa says:

      Yes, but to make sure X goes to 0, the security has to be below the strike in case of Call options and above the strike in case of PUT options.

      • Hari says:

        Hi Karthik bro,
        In Buy side, If premium on particular day(lets say before 10 days or near to expire) is more than settlement i.e exercise amount then is it better to take the premium or is there any incentives if I let my ITM to expire and then exercise .

        Thanks bro

        • Karthik Rangappa says:

          There is no guarantee that the option will remain ITM upon expiry. If you are a short term trader, better to book profits when you see it on the table!

  32. aehsan4004 says:

    dear mr. karthik ,

    after a very very very long-time , something / someone has sparked the learning charge in me.

    i entered the learning modules out of necessity with a mindset of boredom , but now i am simply hooked and continuing for fun .

    options clearly are “magical” and many things can be done using them .

    i have developed a belief that options can be used for a secure no-risk,low-risk trading/investing .


    for example i am long on USD OCT 15 AT 66 .0000 . if price goes down i make a loss .
    but what if i also go LONGPUT same script at 66.0000 ?

    as per my thinking . the loss i make in futures ,is covered by profits in options and vice-versa .

    i would like to know your comments .


    long on USD OCT 15 FUT at 66.0000

    and LONG PUT same script at 67.0000

    what happens on expiry ,in between ?

    • Karthik Rangappa says:

      I’m glad to know that Varsity has ignited your learning enthusiasm. Yes you are right about Options, lots of possibilities with these instruments.

      Yes you can hedge your future positions with Options. Both the examples you quoted are classic long future + long put hedging strategy….and both of them are very similar. Buying 66 PE or 67 PE does not make much difference.

  33. jaganathan says:

    Thank you so much for the lessons and really so easy to learn .
    I have one doubt .
    9.3 Delta for call option.
    spot price = 8288
    strike price = 8250
    premium = 133
    delta = 0.55
    expected to reach 8200
    decline (8200-8288) = -88

    -88*0.55 = -48.4

    133 – 48.4 = 84.6

    spot price = 8288
    strike price = 8300
    premium = 9
    delta = -0.2
    expected to reach 8200
    decline (8288 – 8200) = 88

    In first case decline is in negative value(8200 – 8288) and in second case decline is in positive value(8288 – 8200) , but both have same scenario . please explain why there is no negative delta value in call option with some other example. Thanks.

    • Karthik Rangappa says:

      Thats because the delta is lower bound to 0…it cannot go lesser than 0. If it was lesser than 0, it means the option is moving faster than the underlying, which is counter intuitive.

  34. Raju says:

    Dear Karthik,
    I have some doubt , call trading in different value where as put trading in same value , why there is variation in call premium , can you explain this and how to calculate the value ?

  35. Raju says:

    nse option

  36. deepak says:

    hello mr kartik … i want to do option trading ,please guide me with how much (minimum) amount ,i can start with? 2) does option price (example yesterday dr ready 4300 put price was around 53+ and today was around 600+ …) does it move like stock price goes up n down? i mean want to know from a.b.c of live option trading..pls guide..thanks

    • Karthik Rangappa says:

      Deepak this whole module is dedicated towards helping people understand options trading. Suggest you go through this chapter by chapter.

      To trade options minimum amount would be something like 5000/- I suppose (nifty options).

  37. ashok says:

    hi karthik.
    is there zany formula to calculate delta values?? or its consistent?
    for EX
    Nifty @ 10:55 AM is at 8288

    Option Strike = 8250 Call Option

    Premium = 133

    Delta of the option = + 0.55

    do this delta holds good in below case

    Option Strike = 7900 Call Option
    option spot = 7954
    Premium = 36

    whats delta value in above case and how do we derive it?
    once again thanx for your patience for replying all quires

    • Karthik Rangappa says:

      Delta of the option is dependent of the moneyness of the option – the thumb rule is

      Option is ATM , Delta is ~ 0.5
      Option is ITM , Delta is ~ between 0.5 to 1
      Option is OTM , Delta is ~ between 0.1 to 0.5

  38. Avinash Punjabi says:

    Fantastic easy to understand and involving explanation. I have many times tried to study and understand Option Geeks from many sites but the explanation is so boring that I leave it mid way and close the site.
    The difference between other site topics and your is that to understand the other sites the reader has to be an expert but by reading your site explanation the reader becomes an expert.
    i love it.

  39. abhishek says:

    Hi Karthick,

    Just not clear why we should buy option2 and not option 1? In option2 I will have to pay a higher premium and hence breakeven will be farther than in option 1 case?

  40. SARATH says:


  41. shivamrao37 says:

    Karthik bro.. plzz.. update commodity and currency module.. i want to learn how to trade in currency market..and also want to improve my knowledge on commodity market..i think many here many traders who are trading in commodity markets.. want to improve there skills..

  42. Abhilash D M says:

    Hi, Karthik

    understanding option with time principle is making me more tuff to solve the ENIGMA ,, i have an ready excel file with correct quote executed on the Trading Terminal , would lead to give a big junk of open interest to access .. i know there is a big potential behind the fortune gate …… i would strongly request you to give your few minutes of time on skype ,, i feel the place you and me stand here is we are just from skin of a teath .. i would like to share my knowledge with you on TIME ANALYSIS by W D Gann … ( square of 9 method) is generally understood as …

    would be eagerly waiting for your reply ,,,,


  43. mkpatel01 says:

    How to get the delta of an option ? Is it provided somewhere ?

  44. Raman Ahuja says:

    Hello Karthik Sir,
    This module is absolutely perfect for anyone who wants to trade options. But one thing I’m confused about Delta risk is, how it (delta) will behave when price moves other way around.

    For Example, in above screen shots
    At 9:18 AM, NIFTY 8250 Call price was 144, when NIFTY spot was at 8292
    At 10:00 AM, NIFTY 8250 Call price moves up to 149, when NIFTY spot was at 8315 (an increase of 4 points in call premium, I think at that moment delta would be around 0.15 to 0.20)

    My confusion lies in the other side of the trade i.e. what if I have shorted the put option, how much Put Option premium has been reduced between 9:18 to 10:00 ? or what will happen to Delta of put option (will it increase or decrease) i.e.

    If at 9:18 AM, Put 8250 delta would be around -0.45, when NIFTY spot was at 8292 (this put would be slightly OTM)
    At 10:00 AM, Put 8250 delta would be what -0.4, -0.3, -0.2 ?, when NIFTY spot moves to 8315 (now PUT will moves slightly more OTM). My confusion lies in how much value Put option will loose ? In short I’m asking the rate of change in delta when prices moves other way around. I hope I’m not confusion you

    I’m asking this question because when I look at the spread between Bid-Ask prices of options it gives me a sense that option are illiquid and it is better sell first and buy it later, and I don’t have to bother about STT when exchange auto-settle the ITM contracts.

    • Karthik Rangappa says:

      Well, the Put option delta works the same way as the delta of a call, but in the reverse way. So if spot moves up, the call option delta increases and the put option delta decreases. Of course the delta for each strike varies based on the moneyness of the option. I’d suggest you read up further to know more on moneyness. By the way, 80%+ of all the F&O trading happens on options (Nifty especially), so there is ample liquidity in this particular market.

  45. Raman Ahuja says:

    Ok NIFTY it is, I built my misconception on option by looking at RCOM current month option chain.
    As to the question I asked, my confusion lies in the Writing Calls / Puts.

    So going by the example you have mention in this chapter. How much is the change in delta when NIFTY spot moves down from 8315 to 8288. I’m simply asking how much change in delta a call option writer should expect when he/she short the call, since profit is directly related to fall in spot price.

  46. Sudheer says:

    Hi Karthik,
    The content is very crisp and clear with very good examples and thank you for this work.I have one question over the Delta example you gave in the chapter.For the underlying movement of 100 delta of 0.05 and 0.2 will have increased premiums of 5 and 20.So I as as a Option call buyer will need to pay less premium in case of choosing the 0.05 delta right,but you have mentioned the 0.2 delta is better.Am I missing something.Please clarify..

    • Karthik Rangappa says:

      The selection of Option should not really be dependent on the delta. Hence, I would not choose an option with 0.2 over 0.05 just because i perceive 0.2 as a better delta.

  47. Kumaran says:

    Ur. Modules are too good. I think. The so called trainers should go through this module first before charging money Hats off to u sir

  48. Rohit says:

    Great lessons. I’ve question though, I’m not clear on delta of CE cannot be negative. Does that mean, the option premium will never decrease, even if the underlying decreases?.

    • Karthik Rangappa says:

      Yes, in fact this is exactly how a CE functions. When markets increase, the premium of CE decreases.

      • Dheeraj says:

        Hi Karthik,

        Not able to understand why the CE option Premium will decrease, when the market increases. Shouldn’t it be other was round.



        • Kartik says:

          Yup. Thats’s what I would imagine. Call option delta is always positive because there is positive correlation between the price of the underlying and price of the option. In other words as the underlying goes up, the price of the option will go up too. Conversely, as the price of the underlying falls, the option price will fall too (again a case of positive correlation).

          When it comes to put options, there is negative correlation between price of the underlying and option price. Hence the negative sign.

          • Karthik Rangappa says:

            Absolutely, the call premium moves in line with the underlying and the put premium move the other way round.

  49. Ankit says:

    where can i find real time option greek on zerodha kite,pi

  50. Manish Sharma says:

    Please correct the slightly ITM value from 0.6 to 1 to 0.6 to 0.8 in the delta table. At topic 9.4

  51. jagadeesha says:

    how we hedge with f&o with delta

  52. SUMAN says:


  53. sarthak says:

    Hi karthik.
    Amazing stuff written by youand big help in understanding options.
    1 thing I was not sure about, In the table above where delta value is given for ATM, ITM and OTM.
    In The value of ITM, should it be between 0.6 and 0.8 or 0.6 and 1 because for otm it is written the other way around.

    • Karthik Rangappa says:

      Thanks for the kind words, Sarthak.

      Well, if the option is anywhere between ITM to deep ITM, then it can range anywhere between 0.6 to 1. The acceleration of delta slows down when the option traverses from deep ITM to further deep ITM. This is why you will notice a flattish curve towards the tail. The same is applicable to deep OTM to further deep OTM.

  54. rohit sharma says:

    Hello sir
    I want to know about changes in premium
    For example yesterday’s banknifty close was 21640
    Premium for call for strike price 21600 was 100
    and for put it was 60
    Now today banknifty has moved by
    45 points either downward or upward now what
    Would be changes in premium
    I mean will be increment in premium equal to decrement
    in another premium

    • Karthik Rangappa says:

      You need to read up the chapter on Delta and Gamma to get a clear understanding of this. We have it covered in this and the subsequent chapters.

      • rohit sharma says:

        Sir I have read all modules 2-3times
        Today whatever I have knowledge about stock market, just because of you
        I am so grateful to you and to your team
        If we talk about banknifty what I have observed that if tomorrow’s opening is less than 50-60 points in either direction then premium of today’s ATM changes in one way and if opens by more than 50-60 points then in different way
        Why this happens

  55. pravin says:

    sir .. today i buy nifty 9300 PE at 87.30 rs at the time of buying Put option spot was trading at 9305 ,,after 1 hr spot was trading at 9294 and put option is trading at 87.35 ….why this happen…. ideally it should be (9305-9244)*.50+87.30 =92.80 rs …am i right or wrong …or these option greeks are not work in case of intraday ….plz ans …

  56. R. Ganesan says:

    I am slowly taking into option trading even though I have burnt my fingers before. (Experience wasthe best teacher for me into business)

    Now I am trying a strategy though with smaller lots. So far my results are mixed.

    My post here is:
    Nifty Jun 9800 CE on 11th May 2017 was 18.80 (Nifty spot value was around 9450at that time). Of course Nifty was on unexpected upswing for the previous day due to IMD monsoon data tricking in)

    Nifty Jun 9800 CE on 15 May 2017 was 15.45 even though Nifty spot levels are around the same.

    India Nifty VIX value was -0.11 and 0.44 respectively on 11th and 15th May respectively. (This means volatility has increased)

    Then why the option price divergence between 11th and 15th May 2017? Unable to fathom. Is anything I am missing? Your help is appreciated.


    • Karthik Rangappa says:

      Attributable to time decay to some extent, but the bigger reason could be the trader’s lack of confidence that Nifty will go beyond 9800.

      • R. Ganesan says:

        Thanks for your reply.

        Not only option greeks option buyers/sellers should also take overall expectation of the market it seems. Indicators are not absolute, I understand.

        Is it so? In this case, gamma (time variance) could not have depleted so strongly as the contract is of far month. delta is good, vega is OK.

        • Karthik Rangappa says:

          Yes, along with the greeks you also need to consider the overall market sentiment. This makes a difference.

  57. R. Ganesan says:


    May I know what factors vega depend?

  58. Arun K says:

    With respect to your explanation of impact of Delta on premium. in the example where the Delta of first option is 0.05 and Delta of second option is 0.2. Didn’t understand the reason why would a trader be benefited by paying higher premium of 20. Please help explain.

    • Karthik Rangappa says:

      Remember, the delta also showcases the probability of an option closing ITM. For example, if the delta is 0.7, it also means there is a 70% chance of the option closing ITM. So when a trader pays for a higher premium strike, he is looking for a brighter chances of closing ITM.

  59. KOUSHIK T says:

    Hi Karthik,
    I ‘ve a doubt about “Initial value of delta”.
    I’m nowhere nearing to understand B&S model. What I’ve assumed is when spot price meets strike price the delta of that particular strike is 0.5 and say in call option the far most traded OTM stike price’s delta can be considered as zero. Similarly the far most traded ITM strike price’s delta can be considered as 1 and then on basis of relativity like percentile calculation all other strike price’s delta are calculated.
    Is my assumption is correct? Pl shed some light over it.

    Thanks in advance,
    Koushik T

    • Karthik Rangappa says:

      Your understanding of delta values seems to be correct. However, the deltas itself change due to market forces which is captured by the B&S model. You can keep it simple by assuming that the deltas of each strike is more or less an outcome of what the B&S model throws up.

  60. S Sanyal says:

    Hi Karthik,
    If I buy a call option, at first I thought that I will have to wait till the expiry of the contract to actually gain profits or book ‘losses=premium’
    Now with the new information of dealing with the premiums itself to gain profits I have a confusion.
    Lets say I am dealing with NIFTY options for Strike Price 9700 and Spot price 9500 with 30 days to expire. The premium was 160 when I bought the shares and the lot size was 75. After 2 days the premiums rose to 180 with the spot price at 9600 and I sell the contract. Will I gain (180-160)*75 \? or will I book losses of 160*75 as I did not want the contract and sold it before expiry?

    • Karthik Rangappa says:

      You will make a profit of (180-160)*75 = 1500.

      • S Sanyal says:

        That means I am selling my contract to someone else for the current premium price, if I sell the the contract before expiry. But if I chose not to sell it and wait till the expiry then my profits/losses will be based on the theory which you said in the first few chapters of the options module.

  61. Ayush says:

    i) ITM- ATM => 1 To .50
    ii) ATM=> .50
    iii) ATM-OTM => .50 To 0
    Am i right?

  62. Niraj says:

    Hi kartik,
    i have a account with zerodha in the name of my momm. You people are really doing good job of giving guidance and deep & explanation with simply way and good example. i really like zerodha varsity. God bless u people

  63. venu says:


    Where can i find the delta value on kite or nse website

  64. Vinothini says:

    Why is CALL option premium directly proportional to spot price and PUT option premium inversely proportional to spot price?

  65. jay lakhani says:

    i have two question about maruti. price-9647(down from 9705)
    but CE of 9500 was increased by 8000 percent.
    as the stock price came down than why call option of 9500 increased by these much amount.
    2.if i bought call option of M&M with 770 at 11 rs and stock is trading at 757rs.
    as i am bullish on stock and stock goes up and near to 765 the premium is also increase according to delta.but as per our calculation i made profit after 770+11 premium.but as stock goes up and as premium than if i sell my call option on higher premium than it would be profitable deal or not?
    thank you.

    • Karthik Rangappa says:

      1) This can be attributed to the increase in volatility
      2) Remember, an option contract is also influenced by gamma, vega, and theta besides Delta. Hence you need to have a holistic view.

    • Dheeraj says:

      Hi Karthik,

      Could you kindly suggest on the 2nd query:

      If the option contract is sold before expiry (Call Option profitable trade), would the profit will be as follows:

      (Spot – Strike) – Premium Paid * Lot Size


      Difference in Premium * Lot Size

      • Karthik Rangappa says:

        If sold before expiry, then you will always make the difference in premium. Hence, P&L = (Buy price of the premium – sale price of the premium ) * Lot Size.

  66. Arun says:

    We bow you for your efforts . Very beautifully explained . I am following this from chapter 1 . Thank you

  67. Pratheesh Karthikeyan says:

    Hi Karthik,

    Great work as usual but would like to share one genuine concern – zerodha clients who want to sell fat OTM weekly BNF options are restricted due to some LTP percentage regulation. So today i wasnt able to short 26000 pe/29000 ce. Customer care says there is a certain percentage decided early morning which decides how far one can participate in these OTM options. I wonder how/why zerodha doesnt have clients who want to indulge in far OTM strikes.

    i) There is significant activity in these strikes – which indicates other brokerages allow
    ii) As per today’s % informed from zerodha customer care i.e. 4.1%, i could sell 26400 pe which is a slightly more riskier strike. Now ifi want to hedge it with buying a pe of lesser strike, say 26100, i cannot
    iii) It is tedious and impractical calling everyday to support centre and asking for this % (im told this keeps changing daily). Could you please take some steps like putting it on your website (best), send a mail to clients who are interested to do so (better)?

    Looking fwd to hearing from you.


  68. RS says:

    Hi Karthik – Am new to options and trying to learn using zerodha. Must say it is awesome tutorial. I have a query . in the below example which you have given
    “Call Option 1 has a delta of 0.05, Call Option 2 has a delta of 0.2
    Now the question is, which option will you buy?
    Let us do some math to answer this –
    Change in underlying = 100 points, Call option 1 Delta = 0.05,Change in premium for call option 1 = 100 * 0.05, = 5
    Call option 2 Delta = 0.2,Change in premium for call option 2 = 100 * 0.2,= 20
    As you can see the same 100 point move in the underlying has different effects on different options. In this case clearly the trader would be better off buying Call Option 2. ”
    I thought Option 1 is better as the trader will pay lower premium for the same strike price ? why is option 2 better ?

    • Karthik Rangappa says:

      In fact, your decision to buy or sell an option should NOT be based on DELTA. It should rather be based on the opportunity the candlestick pattern (or any other analysis).

      • Ajeet says:

        Hope i am not misunderstood when you suggest to refer the candlestick too.
        I have a query here, If i am to trade on NIFTY options and am to follow the candlestick, which chart shall i refer? is it the nifty, nifty future for the running series or the chart of CE/PE for that particular strike price?
        Say e.g. i plan to buy/sell 10600CE for which i will be obviously following the greeks and trend, and if i am to look at the candlestick pattern then which one shall i refer? shall i refer the chart of nifty50 or chart of nifty running month future chart or 10600CE chart?

  69. Roopa says:

    Really appreciate clear and simple way of explaining these topics. I have a few questions.
    1) Where can we get the quotes of delta, gamma, vega, IV etc on the Kite platform? I know that NSE has the option chain table but even there could not find out the Greeks values.
    2) When we trade an options strategy and are required to take more than one trade in that strategy, do we have to place individual orders for each trade or is there a method by which we input our criteria and the platform executes it simultaneously for multiple trades?
    3) Do you’ll a program where you can mentor us for options trading and how to execute the strategies. Is there a demo platform available where we can practise taking such trades?
    Thanks and Regards.

  70. PRATIUSH KUMAR says:

    Hi Karthik,

    Thanks for such an awesome content.
    Just out of curiosity,
    Lets assume the premium for nifty CE spot @ 10250 is Rs 9 and delta for an option is 0.5 and if nifty falls by 50 points , then going by the definition of delta , the change in premium i.e. (50*0.5 )= 25 will make the premium negative.
    Has the above scenario ever happened?
    Sorry for sounding so naive, i just want to be clear with the content

    Thanks in Advance!! Cheers 🙂

    • Karthik Rangappa says:

      No, the premium cannot go -ve, if you see the Delta is capped between 0 and 1. Also, remember, Delta is just one contributor to the premium, apart from this, there is also Vega and Theta which is contributing to the premium.

  71. Santosh says:

    The line below if from the chapter above:

    Note – 8268 is a slightly ITM option, hence the delta is around -0.55 (as indicated from the table above).
    Here the Strike price is 8300 . This is for a Put option

    How can this be slightly ITM option, as per the explanation of the chapters which says that higher the strike price from an ATM for a PUT option it is ITM, this needs to be a slightly OTM otpion, kindly clarify my understanding or mis-understanding

    • Karthik Rangappa says:

      Santosh, it works like this. For Call options – ITM – ATM – OTM. So all strike below ATM are ITM and all above are OTM. For Put options OTM – ATM – ITM. So all option strikes above ATM are ITM.

  72. Sameer says:

    Where can we view the delta in the options chain and any reference site for the same

  73. Mohit Bilakhiya says:

    Hello sir,
    Can i buy only just call premium and sell it?
    Or i have to exercise it?

  74. Srikanth says:

    Hi, really informative article. I bought infy 1180 pe (lot 600) at 18/- premium. The delta value is -1 and the expiry is this week Thursday. As the delta value is -1, I assumed that even a slight fall of say 2 to 3/- in the underlying share price can bring almost a similar movement. Currently the option is closed at 16. Can I hold it till the expiry or book Profit or Loss? Your advise for this practical test..

    • Karthik Rangappa says:

      Srikanth, the decision to close the trade is completely dependent on your P&L aspirations, I cannot really comment on it 🙂

  75. Srikanth says:

    Please ignore my previous question, as a few values are wrong.

    Hi, really informative article. I bought infy 1180 pe (lot 600) at 18/- premium. The delta value is -0.52 and the expiry is this week Thursday. Currently the option is closed at 16. Can I hold it till the expiry or book Profit or Loss? Your advise for this practical test..

    • Karthik Rangappa says:

      Like I mentioned in your previous comment, this is dependent on your P&L aspirations. However, you need to remember that the effect of Theta on long options will start eating into the premium in the last week of expiry. So from this perspective, maybe you may want to close the position if you are happy with the P&L.

  76. pavan raj shetty says:

    can I know how the brokerage is charged in the currency derivatives segment

  77. devi singh says:

    In nse website and in zeordha website where i can find delta value.

  78. sammir says:

    how do we get Delta 0.55

  79. sammir says:

    hi kartik
    am new to options & trying to trade as per the Tec analysis of charts , but however , i cannot make any profits
    how do the greeks impact the option premium , how to know when to enter trade & exit trade


    • Karthik Rangappa says:

      I’d suggest you read up the concepts and start taking small directional bets. Get used this and then try figuring out the effect on greeks on your option premiums. This will help I guess.

  80. Ashish says:

    Hi Sir
    The link which you are providing to get the Delta value i.e asking the volatility % , Dividend and interest% . Can you please help , from where we can get these figures to put there ?

  81. Ashish says:

    Hi Sir

    As you said to check delta values we should refer

    In that it is asking the values of
    INTEREST (%)
    from where we can get these values for particular index or stock option?
    Please guide.

  82. Ram says:

    Put options
    Case 2: Nifty is expected to move to 8230
    Expected change = 8268 – 8230= 38
    Delta = – 0.55
    = -0.55*38
    = -20.9

    Here wouldn’t it be accurate if we subtract the other way round ,that is 8230 – 8268 = – 38 .So the premium automatically comes positive as well ,
    -0.55 * -38 = 20.9. There it will be added anyway ,.instead of having a minus sign and still adding the value .

    • Karthik Rangappa says:

      What about the writer?

      The point is to convey that the premium of Put option increases with the decrease in the spot price.

  83. L. Kamalaksh Rao says:

    In a reply to Richa bohra, you have stated that on a bought option, profi ts will be credited on expiry day. I thought since the option was held till expiry heavy STT will be charged on the squar ed sold option.
    Also on an already short option STT would have been deducted normal,. 05percent. So on squaring on ex piry day, there should not be exorbitant STT.
    Pl clarify

  84. Edward says:

    In the first example…when 8288 falls to 8200 and premium is 0.55….
    Caluclations are -80×0.55
    But when delta is negative
    You take 80 vlaue as positive even though it decreases in call option.
    So calculation will be
    -88×-0.2 =-17.6
    *I am really confused on this now.

    • Edward says:

      My next confusion is lets consider if in long call the stock value falls from 8200 to 7200 . And delta is 0.5 and premium is 40 at 8200. The. Fall in underlying i.e. -1000*0.5 is -50
      Then premium comes in negative….how is this possible coz you said premium cant be negative.

    • Karthik Rangappa says:

      Edward, remember this –
      1) Call option lose value when the underlying drops in value. Delta is +ve for call option.
      2) Call option gains value when the underlying gains in value. Delta is +ve for call option.
      3) Put option gains value when the underlying drops in value. Delta is -ve for put option.
      4) Put option loses value when the underlying gains in value. Delta is -ve for put option.

      Given this, take the increase in points in underlying as +ve and the decrease in underlying as -ve.

  85. Bharath N says:

    Instead of making delta -ve for put options it would be simple to have them positive and to consider following formula for

    New premium for put = old premium + ( strike – spot) * positive delta

    Here if spot decreases below strike ,then strike > spot, overall premium is increment

    If spot increases above strike then strike < spot, hence overall premium decreases

  86. Akshay says:

    The following example should help you understand this better –

    Nifty @ 10:55 AM is at 8288

    Option Strike = 8250 Call Option

    Premium = 133

    Delta of the option = + 0.55 How you got delta value 0.55?

  87. NARASINGARAO says:

    Very good info on delta. The delta factor influence on option price is illustrated with nice examples. Easy to understand and grasp.

    Very nice info.

  88. Jasdeep singh says:

    Why Delta for ITM option is high and less for ATM option?

  89. Srinathjayanna says:

    Sir in bs calculator we enter spot price,strike price,expiry date, volatility, dividend and as a final output we get some values for ce premium,pe premium is it those values on expiry the premiums will be trading exactly and what about those delta values here suggesting.

  90. gau says:

    what will be the nu premium value if the nifty has fallen say 300pts.

  91. CHIDAMBARAM V says:

    Hi Sir,
    why is the delta varies for different moneyness of options? Why can’t it be same for all? Why is this disparity for different moneyness?

  92. Aniruddhsinh Rathod says:


    In the explanation of why delta cant be less than zero, In the scenario 2 instead of -0.2 if you put -0.1.the resultant premium would come to +0.2. can you explain that bit further? does it has to do anything with the volatility or premium decay?


    • Karthik Rangappa says:

      But then it cannot be generalized right? as in it can work for few -ve values and not for few others?

      • Aniruddhsinh Rathod says:

        I mean from my general observation it happens all the time in NF and BNF options.The prices are going one way but premium of option will go in opposite direction (for small amount).


        • Karthik Rangappa says:

          This is because the premium is not just dependent on the direction of the trade but also on various other parameters such as volatility, time to expiry etc.

  93. Sachin Jaiswal says:

    I have a query please solve this. (example)
    Cipla spot price is 556.
    I have short 560 CE at a premium of 14.7 and 560 PE @ 17.2 (for June expiry)
    if Cipla is moving upward to 600 or if Cipla is down to 520.
    what will be an effect on my trade?
    Is it the right strategy to trade.
    Please clarify

  94. tangudu neelakantha says:

    hi Karthik

    first of all your material is awesome. keep writing.

    you mentioned the change in nifty prices for the calculation in a change in the value of premium but when you considered the example 2 of call option delta analysis you took the net difference as negative ie -88.

    Nifty @ 10:55 AM is at 8288

    Option Strike = 8250 Call Option

    Premium = 133

    Delta of the option = 0.55

    Nifty @ 3:15 PM is expected to reach 8200

    What is the likely premium value at 3:15 PM?

    We are expecting Nifty to decline by – 88 points (8200 – 8288), hence the change in premium will be –

    = – 88 * 0.55

    = – 48.4

    but later on in put option example, you considered the net difference as positive.

    Spot value 8268
    Nifty is expected to move to 8230

    Expected change = 8268 – 8230

    = 38

    Delta = – 0.55

    = -0.55*38

    = -20.9

    Current Premium = 128

    New Premium = 128 + 20.9

    = 148.9

    I am not able to understand the logic behind the two different cases.

    • Karthik Rangappa says:

      For Call option the delta is +ve meaning, with an increase in spot price the delta gets added and with a decrease in the price, the delta reduces. Likewise, for a PUT option, if with an increase in spot price the delta reduces and with a decrease in the price, the delta increases.

  95. Harsh Singh says:

    Good afternoon Karthikji

    What I discover is one pattern of options trading amongst institutional investors or some smart professional traders is that they sell ITM calls & puts. This is beyond our retailers imagination but from OI analysis & some interviews I read (even on international websites) I came to understand this. Only thing I want to ask is your opinion in following points

    1)Supose Bank of Baroda is trading at Rs 100 approx so why these smart traders sell ITM put(or Calls for that matter) at 102.5 PE & not OTM or far OTM. Is it because to negate high premium lose due to DELTA EFFECTS ?? (as u told that ITM premium moves almost in tandem with Spot)
    2)From above eg ATM has little less oi standing or addition as compare to immediate ITM or OTM ? So it’s to avoid gamma effect. Am I right here
    3)From ur trading experience what u think is right… is it better to sell slight ITM options or far OTM options (calls/puts) for better risk management as spreads (not naked)?? [only ur wise opinion, kindly don’t take it as trading advice I’m taking :)]
    Thanking you for your time 🙂

    • Karthik Rangappa says:

      Harsh, irrespective of who is trading, selling naked deep ITM options is not a good idea. If the institutions are selling it, then they must have a cover for it.

      1) Like I said, a naked short ITM position is unlikely. They would be selling this as a spread
      2) If you are selling, then naked OTMs are the best bet.

  96. Harsh Singh says:

    Good evening Karthikji
    No u’d not read properly my query dear sir. I’d not mentioned anywhere to sell naked options of ITM nor will I take as margin is quite high too.
    What is the advantage of selling ITM options with covered selling compared to OTM. Is there any Greeks benefits?

    Your opinion on this query I needed. Sry for asking again. Thanking u 🙂

    • Karthik Rangappa says:

      Ah, ITM options have higher deltas, which means that for every one-point move in the underlying, we have a near 1 point change in the premium. THis means that the ITM options behave like a futures contract and in fact, can be used as a proxy for futures.

  97. Abhi says:

    Hi Kartik,

    This content has helped me greatly.
    I have a doubt, regarding topics covered before this,
    Is it possible to explain the following wrt the Ajay and Venu example?
    1) Cash settlement
    2) Trading on premium before expiry of contract

    Please help wrt what happens to the underlying asset i.e. land, does it change hands in cash settlement?
    What happens to underlying asset i.e. land when option is bought and sold based on premium.

    Thank You in advance 🙂

  98. Abhi says:

    Also, In the case of trading on premium, what is the role of the call option seller (Venu)?

  99. Mo says:

    I think there is a correction in Delta for Call Option- “Sc. 2 When Delta is below zero”
    Delta= -0.2
    Nifty changed from 8288 to 8200 = -88
    Therefore, change in premium = -88*-0.2 = + 17.6
    Thus, new premium = 9+17.6 = 26.6
    Since premium is increasing with decrease in underlying, it is impossible for delta to be negative.
    Am I wrong? Since you haven’t taken the negative sign for 88 into consideration.

    • Karthik Rangappa says:

      Think of it in terms of the PUT options. Premiums increase with the decrease in the spot price right? This is a positive effect on the premium, which is what gets captured in the math above.

  100. sumeet says:

    Hi Karthik,
    Thank you very much for your effort.

    Just want your view … when I am very sure for any stock/ option to go up , in that condition which one I should prefer … call option vs future

  101. Harsh Singh says:

    Good morning Karthikji
    I’ve one question.
    1)Since Futures delta is one. How should I hedge it with say Call options when I’m say long in Futures ?
    2) This one is most important. Suppose I hedge Reliance or Nifty Long Futures with two 0.5 delta call options. But the problem is that when the spot moves up so is the delta and say the combined short call options delta turns 1.5 on robust upwards movement(since many times on market opening things r hardly in our control we all know). So essentially I’m at loss by 0.5 delta since Futures delta anyway remain one only ?? So how should I deal with this problem
    Kindly explain with examples thoroughly esp 2nd point.
    Thanking you for your time & will be pleased with ur wise opinion. Hv a great day 🙂

    • Karthik Rangappa says:

      1) Since futures long is +1 delta, you will have to offset this with -1delta, hence 2 lots of selling ATM call (each with delta of -0.5) will help you hedge the position
      2) Yes, you will have to adjust this especially if you intend to carry it overnight. You can ignore it for intraday

      Hope that helps 🙂

  102. sridhar says:

    how is delta calculate pls illustrate with example

  103. Rashika says:

    I think in the put option example here,
    Case 2: Nifty is expected to move to 8230

    Expected change = 8268 – 8230

    = 38

    Delta = – 0.55

    = -0.55*38

    = -20.9

    Current Premium = 128

    New Premium = 128 + 20.9

    = 148.9

    It’s better to calculate expected change as
    Delta= -0.55*-38 =20.9
    Net premium =128+20.9=148.9

  104. Srijita Roy says:

    First let me quote a portion of this chapter, “Call Option 1 has a delta of 0.05

    Call Option 2 has a delta of 0.2

    Now the question is, which option will you buy?

    Let us do some math to answer this –

    Change in underlying = 100 points

    Call option 1 Delta = 0.05

    Change in premium for call option 1 = 100 * 0.05

    = 5

    Call option 2 Delta = 0.2

    Change in premium for call option 2 = 100 * 0.2

    = 20

    As you can see the same 100 point move in the underlying has different effects on different options. In this case clearly the trader would be better off buying Call Option 2. ”
    Sir my question is as a call option buyer we should always prefer low premium isn’t it? Then why are we selecting option 2 in this case I didn’t understand.

    • Karthik Rangappa says:

      Hmm, the selection of strike should not really depend on just the premium. You should look at greeks as well, such as the delta and the theta.

  105. ROHIT SHARMA says:

    Sir in Black & Scholes formula what is ” Risk free interest rate”

  106. Anil says:

    Sir in black scholes model, how to determine dividend value for Nifty or bank nifty to input in calculator

  107. Sachin says:

    Hi Karthik,

    First of all, many thanks for such a wonderful writeups and sharing knowledge on all these topics.

    I’m really confused by your response to query on section 9.5, “Delta for a Put option”. Strike is 8300, Spot is 8268. Option is Put. Its mentioned as slightly ITM. Shouldn’t it be slightly OTM?

    • Karthik Rangappa says:

      No, 8300 PE is slightly ITM considering spot is at 8268. All strikes below 8268 are OTM and higher are ITM.

  108. Sachin says:

    Got it. Revisited moneyness topic too and is clear now.

  109. Jayadevan.T.J says:


    The subject is presented in an excellent manner. Thanks from the bottom of the heart to You and Your assistant who had taken these screenshots. I know it is a tedious job. Thank you again.


  110. Satish Baichwal says:

    Hello Sir
    Thanks for the education you are giving. All the content are so arranged that a novice can also understand the subject. Superb explanation power.
    May I know where can we find the DELTA value from?

  111. Satish Baichwal says:

    Thank you Sir for your prompt reply.
    Satish Baichwal

  112. Sanchit Goel says:

    Call Option 1 has a delta of 0.05
    Call Option 2 has a delta of 0.2
    I these two call options the later one would have bigger premium then how come it is suitable for buying, should we not prefer to pay less premium? If there is something I have missed please let me know.
    BTW these articles are just mind blowing..
    Thank you

    • Karthik Rangappa says:

      The amount you pay as premium depends on many factors –

      1) What is the volatility?
      2) What is your expectation of future volatility?
      3) What is your expectation of the price movement?
      4) Time remaining for expiry

      So the delta is just one parameter to look at. I’d suggest you read the rest of the chapters to connect the dots.

  113. Sanchit Goel says:

    Sure I will

  114. surendra says:

    Hi, Where can i find respective Option delta in the Option china

  115. Shrey says:

    Can we derive any conclusion about movements of underlying based on options chart and then put it to use in spot-market trading?

  116. Aso says:

    Sir, for the 9.5 topic
    (the Delta for Put option)
    Note- 8268 is a slightly ITM option.
    *i think it should be, 8268 is a slightly OTM option* because strike price is at 8300. or am i wrong? i am not sure.
    By the way, i love your teachings. Thank you so much. God bless you.

    • Karthik Rangappa says:

      I’m glad you liked the content here 🙂

      Since the strike is 8300 PE, it is slightly ITM as the spot is at 8268.

  117. Aniket says:

    Is it possible to calculate accurate delta by comparing the attributes of 15 min candle of option and that of underlying.

    Say for a OTM CE, 15 min candle had a movement of 30 points bullish whilst the underlying concluded with 100 points bullish move.

    Thus giving a 30 percent change i.e. 0.3 delta

    • Karthik Rangappa says:

      Have not tried that, but you can use a B&S calculator to find out precise delta, so why reinvent the wheel 🙂

  118. Topesh says:

    Hi karthik,
    Really very beautiful and understandable content.
    My Question.
    Under delta for put option section.
    Case 2: Nifty is expected to move to 8230
    Expected change = 8268 – 8230

    What i thought is expected change will 8230 – 8268 because 8230 is final price.

    New premium = old premium +/- ( delta*expected change of spot price)

    Where as in above formula + for call option because call option premium is directly proportional to change in spot price and – for put option because it is inversely proportional to change in spot price.

    By doing this also the final premium will be same compare to your calculation because negative value of delta will take care.

    Please correct me if my approach is wrong.

    • Karthik Rangappa says:

      That’s right, the -ve sign associated with a change in underlying is multiplied with the -ve sign associated with the put delta and the resultant is a +ve change in put premium for the given change in the underlying.

  119. Nitin says:

    Sir where can we get the delta value of the call option. I can’t find them on kite, kindly help!

  120. Aditya Aryan Sonker says:

    should we exercise an American Call option before an ex-dividend date if yes then what are the factors we should consider….?

  121. Sanjeev Patel says:

    Due to the quality of content I have switched to reading this rather than watching Youtube Videos.

    My Question is .
    1. If I have Sold PE In case the margin get short will I get some warning and how much time will I get to add funds?
    2. In options and futures which time is considered as expiry explain through an example. What will be the charges/fine after expiry?

    3. Future : If I have bought future of a stock(lot size 500). It requires a margin of around 1.5 Lakh. So If I buy a lot (say at 1500 )and sell after 15 days ( at 1550). Will my profit calculated by
    a) the Investment (margin) 1,55,000(new future value) -1,50,000(old future value)= 5000
    b) with respect to the total value of the lot which is 7.5 Lakh. ( Profit 50*500 = 25000) where I have only paid/blocked 1.5 lakh only.

    4. How to roll over the future to next month on expiry?

    5. How to take delivery of the stock through Futures and Options.

  122. Aditya Aryan Sonker says:

    I know that American options are not applicable in India but it is something that came up while I was studying for FRM so can you kindly answer it

    “should we exercise an American Call option before an ex-dividend date if yes then what are the factors we should consider….?”

    • Karthik Rangappa says:

      That depends on both stock and F&O settlement criteria. For example, if this was in Indian context, yes, it would make sense as you would get the stock before record date to received corporate benefits.

  123. Vikram Rao says:


    I have observed one thing on the sensibull platform, the sum of Call Delta and Put Delta (ignore the +ve and -ve symbols) is 1. Lets say if the call delta is 0.2 and obviously the put delta will be -0.8; Doesn’t it make sense to buy PUT if the underlying is going down (I Know selling a call option has higher probability of making profits however using the higher delta on the put side we can make more money by buying PUT rather than sell call, almost 1:4. (Of course we need to be sure of the direction of the underlying) .

    Am i making sense/ is my understanding correct?


    • Karthik Rangappa says:

      Vikram, call delta os 0.2, does not mean the PUT dealt is -0.8. But I dint get the other bit of your question. Can you add more context to this, please? Thanks.

  124. Arun says:

    If Min value of delta for CE is zero. How does the premium reduce for long call when spot goes below strike.
    Ex Nifty 8200 CE long call
    Premium 10
    Spot 8145
    Assume Delta 0
    Spot moves to 8090

    The new premium will be definitely below 10.
    So, how is the premium calculated?
    Kindly clarify.
    Thank you

    • Karthik Rangappa says:

      Delta wont be zero, it is will have a non zero value. In this case it could be around 0.3 or 0.35. So for every 1 point move in Nifty, premium will change by 0.3 or 0.35. So you can do the math accordingly.

  125. Vikram says:

    Hello Karthik,

    I am not able to upload the snapshot, however please check the delta values of any strike price in sensibull both call delta and put delta. Its always equal to 1 (I mean if we ignore the + and – symbols next to them)

  126. Narayanan says:

    Hi Karthick.

    Thank you so much for providing endless amount of knowledge through varsity zerodha
    Here goes
    Concept wise Beta & Delta is same right ?
    Beta shows how much percentage the stock will move when compared to index ? And
    delta shows how much percentage the premium will move when compared to the spot price ?
    Am I right ?

  127. Sanjeev Patel says:

    Thanks for your answers. I now have less doubts but I am confused from this answer.
    Future : If I have bought future of a stock(lot size 500). It requires a margin of around 1.5 Lakh. So If I buy a lot (say at 1500 )and sell after 15 days ( at 1550). Will my profit calculated by
    a) the Investment (margin) 1,55,000(new future value) -1,50,000(old future value)= 5000
    b) with respect to the total value of the lot which is 7.5 Lakh. ( Profit 50*500 = 25000) where I have only paid/blocked 1.5 lakh only.

    Your Answer – Yes, that is one of the ways to calculate the profit. The other way is to just take the difference between the buy and sell price of the futures and multiply that with the lot size.
    How can be there more than one ways to calculate profit.
    It would be very helpful if you could tell me through Reliance Example
    CMP is 2172.05
    Margin Required for Future 2,98,021.58
    Lot Size 505
    Lets say In 5 days Price Moves by 21.72 Points to 2193.77 ( i.e 1% increase )
    and I sell it that at that price.
    Now what will be my profit in Rupees? What will be the value of Future lot now.
    Please explain this in detail. As it is the last question which will finalise my strategy.

    • Karthik Rangappa says:

      Buy Price = 2172.05
      Sell Price = 2193.77
      Quantity = 505
      Difference between buy and sell price = 21.72. This means you’ve made 21.72 per share. You hold 505 quantity, hence your P&L = 505*21.72 = Rs.10,968.6/-

  128. Deepak says:

    Hi Karthik, thanks for the article. It’s very helpful.
    I have a question. I see LTP for every option contract in Zerodha. I guess this is the premium.
    For some reason I believe this LTP moves based on the bids and asks and not the option greeks. Correct me if I am wrong.
    If this LTP moves based on bids and asks, then can I use technical analysis of this LTP to take a position?

    • Karthik Rangappa says:

      Thats right Deepak, the LTP moves based on Bid and Ask, but that is just one factor. What largely influences the options is the movement in the underlying itself. Hence you are better off applying TA on the underlying rather than the option contract.

  129. Sridharan Gupta says:


    Plz refer to my trade details below:

    Option – Short call
    Strike price- 2500
    Spot price-2300
    premium- 21
    Days to expiry-20

    If lets says after 5 days the spot price moves to 2400, the option premium will increase and the person who is in contract with me exits his/her postion, will my position get squared off automatically or it will have no impact on my postion?

  130. Samar Ali Warsi says:

    Can we consider the option delta (a rate change in option premium based on the rate change of the underlying) to be similar to a stock or a future’s beta (a rate change of an asset based on the rate change of an index)?

  131. RAHUL AGGARWAL says:





  132. Rahul Aggarwal says:

    Sir my question is about finding the change in the premium so for that I have (multiplied the delta with change in underlying points) and after that I have subtracted with the old premium in the put option. and then the new premium is coming to negative. The change in the premium is more than that of old premium so it is coming negative.

  133. RAHUL AGGARWAL says:

    sir then we will try to avoid such option or the strike price ? or we can take it in such circumstances ?

  134. Ridhima says:

    Do we need to calculate delta or it is available on NSE

  135. MONU says:

    Sir ,I have a positional trade which I have taken one week ago in options .Can I convert that trade into MIS today? If yes then can that be done in both long and short positions? Thank you sir.

  136. kaleeswaran K says:

    In the above case -2, change in value is Minus 38 (-38); only then -38 *-.55=+20.9
    New premium will be 128 + 20.9 = 148.9
    Thank you very much for Deep Explanation ..

  137. vansh says:

    In case 1 of the put option, the delta value is -0.55 which is ATM as per the table. However, you have mentioned that it is slightly ITM. Please check it again!

    • Karthik Rangappa says:

      Strictly speaking, ATM is supposed to be 0.5 for calls and -0.5 for puts. If its higher than 0.5, like 0.55, then it means that it is slightly ITM.

  138. Yash says:

    Hi sir , in the beginning of chapter 9.5 , you mentioned “Note – 8268 is a slightly ITM option, hence the delta is around -0.55” , i think OTM , ITM for an option is classified for strikes by comparing them to spot value . Here 8268 is a spot value not a strike value, i didn’t really understand why that was taken as ITM option.

  139. RAKESH S says:

    Please let me know what is the mistake in this analysis:
    A stock value reduces from 8288 to 8000 during the day. Its premium is 133 and delta is 0.55.
    So its underlying value has reduced by -288 points,so the change in premium will be (-288*0.55)=-158.4.
    So the current premium amount becomes 133-158.4=-25.4

  140. Sumit Vakharia says:

    Hi Sir,

    Where do we get the values of Delta for different stocks? and for different strike price? do we always have to assume based on our experience?

  141. Krunal says:

    This is extremely useful information to have while trading options. For example assume you expect a massive 100 point up move on Nifty, and based on this expectation you decide to buy an option. There are two Call options and you need to decide which one to buy.

    Call Option 1 has a delta of 0.05

    Call Option 2 has a delta of 0.2

    Now the question is, which option will you buy?

    Let us do some math to answer this –

    Change in underlying = 100 points

    Call option 1 Delta = 0.05

    Change in premium for call option 1 = 100 * 0.05

    = 5

    Call option 2 Delta = 0.2

    Change in premium for call option 2 = 100 * 0.2

    = 20

    As you can see the same 100 point move in the underlying has different effects on different options. In this case clearly the trader would be better off buying Call Option 2.

    Why will the trader select call option 2 and not call option 1 as the change in premium is higher in call option 2. Can you please try to guide me?

    • Karthik Rangappa says:

      Its the same explanation, Krunal. The rate of change of delta is higher in the 2nd case, hence its likely to be more profitable.

  142. Krunal says:

    Thank you sir

  143. Ganesh Patel says:

    Here in the example, you considered delta as constant for both the cases(gain and decline in underline).but in the real market delta will get change at every move of underline right and so the calculation ?

    Loving Varisty 🙂

  144. Aarti says:

    Dear Kartik sir,

    You mention that delta for CE will always range between 0 to 1. However, I just checked the Bank Nifty @11:26am (today 7th Oct’20) and the premium at 20500CE is at 2424 while BankNifty is trading at 22807.45. A while ago too I had checked at 10:21am(today 7th Oct’20) at that point in time 20500CE with a spot at 22882.4 was trading at a premium of 2569.15. So essentially the point I am trying to hammer home is, that with a fall in the underlying index by 74.95 the premium for 20500CE fell by 145.15, suggesting a delta of -145.15/-74.95=1.94, assuming a formula of delta as change in premium/change in underlying.

    So does not this prove your hypothesis wrong that delta for CE can only range between 0 to1?
    I may be wrong, but I don’t know where am going astray. Could you shed some light sir?

    Many thanks.

    • Karthik Rangappa says:

      Let’s assume your theory of Delta being any number higher than 1 is true for a bit. Assume, the delta is 2. Now, underlying moves by 1 point, what does that mean? That means the option premium moves by 2 points, which essentially means the premium is moving at a higher rate than the underlying itself. Do you think this makes sense?

      Also, you cannot calculate the delta with the kind of division you’ve illustrated. That does not work that way. Delta is an output from the B&S options calculator.

  145. Gautam says:


    In the above example where one had choices between buying two Call options with delta 0.05 & 0.2 and Nifty has 100 points upwards movement. Why do you say CE with delta 0.2 is better? Wont it mean the premium is expensive?

    • Karthik Rangappa says:

      Gautam, given that the underlying is expected to move just 100 points, the option with delta of 0.2 will react better in terms of P&L.

  146. Sanjay Pandey says:

    Dear Karthik sir,
    Thank you very much for your this knowledgeable, authentic and free course. Really it’s a great initiative by you and team. I think nothing can be better than this.
    Sir would you please explain about one more type of Greek rho.
    Best regards
    Sanjay Pandey, Bangalore.

    • Karthik Rangappa says:

      Thanks, Sanjay, glad you liked it. I left of Rho thinking it is not of much practical use. Will try and put up something on it soon.

  147. Sagar says:

    Thanks Karthik. just wanted understand what does the IV column in Nifty option chain signifies ?

  148. Narendra says:

    Which Value of DELTA you prefer to trade with. ?

  149. Shyamsunder says:

    Very good execution Karthik sir

  150. Vikas Kamboj says:

    Hi Could you please change put delta calculation senario 2 as when underlying expected to decline by 38 point means -38….. and when it will be multiplies by -.55 it would simply converted into a positive value i.e. -.55*-38 = +20.9 and you need not to state that as spot value decline we need to add it will simply add as value is positive…. and in case of positive change from current underlying value product of delta and change would be negative i.e. -.55*x = -.55x and it will simply get subtracted from current premium.

  151. Sarang says:


    I did not follow your answer given to Gautam. When Delta is 0.2, Premium will be expensive. For both 0.05 and 0.2 Delta, spot price will move by 100 points, which is constant. So how option of expensive premium would be more profitable? Would be glad if you elaborate.

  152. Mitul says:

    Cannot find the greek details in varsity application.i downloaded the application.

  153. rajesh mestry says:

    Hello Karthik,

    What a marvellous job you have done !

    I have a query in chapter no. 9.5 Delta of a put option – In the example you have mentioned that:
    Note – 8268 is a slightly ITM option, hence the delta is around -0.55 (as indicated from the table above). I think as it is a put option and strike is 8300, 8268 should be slightly OTM and Delta should be around -0.45. Kindly revert.

    Rajesh Mestry

    • Karthik Rangappa says:

      Thanks Rajesh, hope you will continue to like the content 🙂

      The spot is 8268, lower than 8300, hence 8300 PE is slightly ITM, with an intrinsic value of 32.

  154. rajesh mestry says:

    Thanks dear, Gochha !

    I mistake, I misunderstood as 8268 as stike price hence considering 8300 as spot price. Now very well understood

  155. parth joshi says:

    i think there is mistake in topic of”delta for put option” example no.2
    you first calculate underlyingprice-spotprice
    i know why yo do this,
    but in all other delta example you first calculate spotprice-underlyingprice(when option buy).
    i think it create some confusion in reader’s mind.

  156. Harish says:

    The below note in Section 9.5 seems incorrect.
    –>Note – 8268 is a slightly ITM option, hence the delta is around -0.55 (as indicated from the table above).

    8268 was the Spot Price. Delta should be based on Strike Price, which is 8300. Right ?

  157. Atul says:

    Dear Kartik Sir,
    Let’s take one example
    Friday Reliance closed at 2080.30 (cash)
    25.02.21 expiry PE at Strike price 1,600 (Deep OTM) premium was Rs 0.20
    Today Reliance drop by Rs 50 and presently trading at 2,030 and premium dropped to Rs 0.15
    This drop of 0.05 is due to time decay but my question is here delta ( say at leat at 0.05 ) did not work. I mean at 0.05 delta with price drop of Rs 50, premium should have been increase by around Rs 2.50 but that did not happen.

    Does it mean, delta worked at 0 and is this because it is near expiry?

    If this price drop happened 10 days before , the effects of Rs 2.50 would have worked?

    Is delta and Theta have co relation?
    I mean, delta drops as time decay and over the price VS delta proportion?

    I will appreciate, if you answer

    • Karthik Rangappa says:

      This is because of the expiry since we are very close to expiry, the effect of theta is much higher than the effect of any other variables (especially true of deep OTM options). FOr this put to move, the drop in price has to be significant, like 200-300 Rupee drop. In such case, delta will overtake theta.

  158. Pankiras Cleetus says:

    Refer to 9.5 – Delta for a Put Option

    “Note – 8268 is a slightly ITM option”

    You mentioned that Strike is 8300. If so, will 8268 be slightly ITM or slightly OTM? Please clarify.

  159. Malathy Ramanan says:

    I have a trading account with Zerodha. Please inform from which website can I get the Delta for Different strike prices for Call and Put

  160. Utsav says:

    Nifty is expected to move to 8230

    Expected change = 8268 – 8230

    = 38

    Delta = – 0.55

    = -0.55*38

    = -20.9

    Current Premium = 128

    New Premium = 128 + 20.9

    = 148.9
    Sir in above Ex shouldn’t we do 8230-8268
    and than 128+21.9 = 148.9

    • Karthik Rangappa says:

      Not really, Utsav, we just take the difference in the spot change. The delta indicates the sign anyway.

  161. Sakthivel says:

    Expiry day what I am doing?
    How to exit?
    If exit what is happening?
    If not Exit what is happening?

    • Karthik Rangappa says:

      What you will do, depends on what you want to do. To exit, you can press the exit position button on the terminal. If you don’t exit, it will be settled by the broker.

  162. Priyank Shah says:

    Why the delta in Put Option is between -1 and 0? While I understand the it cannot go lesser than -1, what if I take the delta say 0.55 (greater than 0)?
    The calculation is as below
    Nifty Spot – 8268
    Expected – 8310
    Expected change – 42
    Delta value = 0.55*42 = 23.1

    Ideally we should subtract the value from the premium as the underlying is increasing in a put option. If we do that, we get 104.9 (which was like the first case).
    There’s a confusion here.
    Can you please clarify?

  163. Krishna Nair says:

    Hey Kartik, how to login to Varsity(on a PC or through browser), do you need a Zerodha account for logging in? Also, why don’t comments work on the app? I didn’t even know that comments were an option until I started using Varsity on my PC.
    Thanks a lot

    • Karthik Rangappa says:

      No need to log in for VArsity web, you can comment without one. however, we need login for the app to ensure we maintain your progress.

  164. Vipul says:

    Could you elaborate on
    `As you can see the same 100 point move in the underlying has different effects on different options. In this case clearly the trader would be better off buying Call Option 2.`

    • Karthik Rangappa says:

      This means, based on the moneyness of the option, the premium may vary for the very same movement in the underlying.

  165. Vipul says:

    Why would he be better off buying call Option2 is my question.

  166. Jaydeep shudra says:

    Hello kartik, Can I buy a call option at 9:20 Am and sell it on the same day (3:20pm)?

  167. Robin Sethi says:

    Note – 8268 is a slightly ITM option, hence the delta is around -0.55 (as indicated from the table above) : From the module

    If 8300 is the strike of the PUT OPTION, then won’t 8268 be slightly OTM option?

  168. Robin Sethi says:

    Yes, it’s clear. Got confused in that bit. Thanks 🙂

  169. Deep says:

    Hi Karthik, I had one query. In the first example of this chapter of Nifty, 8250 CE is ATM considering Spot price 8292. So, the Delta should be around 0.5. Now, if the underlying moves to 8315, it’s a (8315-8292)=23 point upward move, so the premium should also move (144*0.5)= 72 points up, right! Whereas, the new premium is just 149.40. Why is that?
    It’s middle of the month and I understand that other greeks are effecting the price too. Can you elaborate what is happening here like what other greeks are effecting the price and how? That would be a great help. Thanks.

    • Karthik Rangappa says:

      That is true assuming only delta moves and all other greeks are constant. In reality, all greeks exert a force on the premiums which you need to factor in.

  170. Umamaheswaran says:

    In the example given for delta of 0.05 and 0.2, I assume the call buyer will take the one with lower premium. However the example mentions that the user will buy call for costlier delta 0.2.. Could you please explain

    • Karthik Rangappa says:

      This depends on the larger context of the market and expectations right? I’ve tried to explain this in the chapter itself.

  171. Avinash Singh says:

    Hello, It is mention here that value option can’t change more than value of underlying, i.e. delta value can’t be more than 1.
    But on 28.05.21
    change in Havells spot price is -1.7 rs ( change from 1019.8 to 1018.1)
    But change in Havells jun ce 1060 is -3.35 rs( change from 27 to 23.65)

    • Karthik Rangappa says:

      Avinash, you need to compare the delta of the option, not the absolute price change of spot and the premium.

  172. Soumen says:

    Excellent explanation. Thx.

  173. Daksha T says:

    Hi, is it possible to cover Credit default swap in detail? It’s a request.

  174. Sam says:

    Sir can u plse provide us pdf of each modules

  175. Sam says:

    Sir where?

  176. Sam says:

    How do we get excess to it??

  177. Sam says:

    I have found the pdf’s.

    But there is no pdf for modules12 and 13

  178. Bhanu Thapa says:

    As per understanding section 9.5 correction require

    Case 2: Nifty is expected to move to 8230, spot price is 8268
    Expected change = 8230 – 8268 = -38
    Delta = – 0.55
    Premium expected to change by = -0.55*-38 = 20.9
    Current Premium = 128
    New Premium = 128 + 20.9 = 148.9

    • Karthik Rangappa says:

      Checking this, btw, I think this was discussed and clarified in the comments above. Can you please check?

  179. laxman says:

    option 1 delta 0.05 , change in premium for every 100 points in underlying = 5
    option 2 delta .2 , change in premium for every 100 points in underlying = 20
    we have to pay more for buying call option 2,
    why it is better to buy 2 as given in example

    • Karthik Rangappa says:

      Which option is better depends on the market situation. If there is more time to expiry and you are bullish, then option 1. If there is not so much time to expiry and you are bulish, then maybe option 2.

  180. RISHABH PATEEL says:

    I have a similar question, ” WHO DECIDES VALUE OF OPTION PREMIUMS? which came into my mind when I read this” Who decides the value of the Delta?”

    • Karthik Rangappa says:

      Rishabh, these are all market-driven. Its collectively driven by the market. Very similar to vegetable prices. For example who decides the prices of onions? Its market-driven right?

  181. Pinaki Nandy says:

    Sir where can i get delta, iv, theta of an option strike price
    Pinaki Nandy

  182. Manohar S says:

    Hi Karthik

    Well explained. This so much for your efforts

  183. Shed says:

    😂😂I was reading so deeply when I red keytakways from this i was like 😔ohhhh this end here

  184. Ronak Jain says:

    How you came up with delta 0.55 in the example of Nifty you gave ? how to find that or calculate that ?

    • Karthik Rangappa says:

      I’ve explained how delta varies based on the moneyness of the option. Request you to kindly check that. Thanks.

  185. gurjeet says:

    sir so can we conclude that buying an deep itm option is better than buying future (considering intraday), even i will need less amount to get equal benefit. and even the loss will be same in both the scenario.

  186. Prerana says:

    * Call Option 1 has a delta of 0.05
    * Call Option 2 has a delta of 0.2
    Now the question is, which option will you buy?
    * Change in underlying = 100 points
    – Call option 1 Delta = 0.05
    Change in premium for call option 1 = 100 * 0.05 = 5
    – Call option 2 Delta = 0.2
    Change in premium for call option 2 = 100 * 0.2 = 20

    Could you please explain how option 2 is better?

    • Karthik Rangappa says:

      Prerana, the decision to buy or sell an option should not be dependent on the delta, rather should be dependent on what you expect from the market.

  187. Anil dhumale says:

    Thanks for sharing valuable information sir

  188. Gosai ram says:

    Best explanation #tradingwithbooks

  189. sakshi says:

    where can we see the Delta value of option of a underlying stock

  190. Saurav Singh says:

    Hello nikhil, I wanted to know that how can we know (Volatility% and interest%) when we calculating Delta value by using B&S calculator

  191. Raja Sen says:

    Hello Nikhil,
    First of all thank you for such useful contents to understand options. I have query on the following sample scenario (in quotes below) discussed under the heading “Delta for call option”.
    “For example assume you expect a massive 100 point up move on Nifty, and based on this expectation you decide to buy an option. There are two Call options and you need to decide which one to buy.
    Call Option 1 has a delta of 0.05
    Call Option 2 has a delta of 0.2
    Now the question is, which option will you buy?
    Let us do some math to answer this –
    Change in underlying = 100 points
    Call option 1 Delta = 0.05
    Change in premium for call option 1 = 100 * 0.05 = 5
    Call option 2 Delta = 0.2
    Change in premium for call option 2 = 100 * 0.2= 20″
    As you can see the same 100 point move in the underlying has different effects on different options. In this case clearly the trader would be better off buying Call Option 2.”

    Since the payoff for call option buyer is max (0, spot – strike) – premium, wouldn’t it be helpful for the trader to opt for low change in premium (i.e. 5) as premium reduces the payoff overall? Please help on this as I have hit a roadblock here.

  192. Anil says:

    Hi Karthik,

    I have a query. Here is the example you mentioned.

    Nifty @ 10:55 AM is at 8288
    Option Strike = 8250 Call Option
    Premium = 133
    Delta of the option = + 0.55
    Nifty @ 3:15 PM is expected to reach 8310

    and then calculated the new premium as 133 + (8310-8288)*0.55 = 145.1

    What this means is that @10:55AM, the nifty spot price is 8288 and to buy the 8250 Call option, one has to pay 133 rupees as premium so that at the end of contract expiry, buyer can get nifty at 8250 rupees irrespective of spot price of nifty in market.

    If suppose, the nifty spot price increased by 300 points by @3:00PM
    Nifty spot price: 8288 + 300 => 8588
    New Premium: 133 + 300*0.55 => 298

    So now, to purchase nifty at the end of contract at 8250 rupees, one has to pay 298 rupees of premium. If you see here, current spot price (8588) > new premimum (298) + strike price (8250).

    Is it possible to have this type of situation in market where the current spot price is greater than premium + strike price?
    If yes, then won’t the buyer have higher chance of getting profits? He makes profit if nifty stays at same price (or) moves up.
    which is a contradiction to what we learned in call options theory where seller have more chance of getting profits than the buyer.

    I know these numbers are used as an example, but point that I want to ask is “Is it possible in market where the current spot price is greater than premimum + strike price”?


    • Karthik Rangappa says:

      Yes, its very possible for the spot to be higher than strike + premium. But remember, there is also a time component that keeps eating away the premium with the passage of time, so all else equal the premium will come down.

      I’d suggest you take a look at the option chain to see how the premiums are behaving wrt to spot price, you will understand this better.

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