Module 5 Options Theory for Professional Trading

Chapter 14

Theta

161

14.1 – Time is money

Remember the adage “Time is money”, it seems like this adage about time is highly relevant when it comes to options trading. Forget all the Greek talk for now, we shall go back to understand one basic concept concerning time. Assume you have enrolled for a competitive exam, you are inherently a bright candidate and have the capability to clear the exam, however if you do not give it sufficient time and brush up the concepts, you are likely to flunk the exam – so given this what is the likelihood that you will pass this exam? Well, it depends on how much time you spend to prepare for the exam right? Let’s keep this in perspective and figure out the likelihood of passing the exam against the time spent preparing for the exam.

Number of days for preparation Likelihood of passing
30 days Very high
20 days High
15 days Moderate
10 days Low
5 days Very low
1 day Ultra low

Quite obviously higher the number of days for preparation, the higher is the likelihood of passing the exam. Keeping the same logic in mind, think about the following situation – Nifty Spot is 8500, you buy a Nifty 8700 Call option – what is the likelihood of this call option to expire In the Money (ITM)? Let me rephrase this question in the following way –

  • Given Nifty is at 8500 today, what is the likelihood of Nifty moving 200 points over the next 30 days and therefore 8700 CE expiring ITM?
    • The chance for Nifty to move 200 points over next 30 days is quite high, hence the likelihood of option expiring ITM upon expiry is very high
  • What if there are only 15 days to expiry?
    • An expectation that Nifty will move 200 points over the next 15 days is reasonable, hence the likelihood of option expiring ITM upon expiry is high (notice it is not very high, but just high).
  • What if there are only 5 days to expiry?
    • Well, 5 days, 200 points, not really sure hence the likelihood of 8700 CE expiring in the money is low
  • What if there was only 1 day to expiry?
    • The probability of Nifty to move 200 points in 1 day is quite low, hence I would be reasonably certain that the option will not expire in the money, therefore the chance is ultra low.

Is there anything that we can infer from the above? Clearly, the more time for expiry the likelihood for the option to expire In the Money (ITM) is higher. Now keep this point in the back of your mind as we now shift our focus on the ‘Option Seller’. We know an option seller sells/writes an option and receives the premium for it. When he sells an option he is very well aware that he carries an unlimited risk and limited reward potential. The reward is limited to the extent of the premium he receives. He gets to keep his reward (premium) fully only if the option expires worthless. Now, think about this – if he is selling an option early in the month he very clearly knows the following –

  1. He knows he carries unlimited risk and limited reward potential
  2. He also knows that by virtue of time, there is a chance for the option he is selling to transition into ITM option, which means he will not get to retain his reward (premium received)

In fact at any given point, thanks to ‘time’, there is always a chance for the option to expiry in the money (although this chance gets lower and lower as time progresses towards the expiry date). Given this, an option seller would not want to sell options at all right? After all why would you want to sell options when you very well know that simply because of time there is scope for the option you are selling to expire in the money. Clearly time in the option sellers context acts as a risk. Now, what if the option buyer in order to entice the option seller to sell options offers to compensate for the ‘time risk’ that he (option seller) assumes? In such a case it probably makes sense to evaluate the time risk versus the compensation and take a call right? In fact this is what happens in real world options trading. Whenever you pay a premium for options, you are indeed paying towards –

  1. Time Risk
  2. Intrinsic value of options.

In other words – Premium = Time value + Intrinsic Value Recall earlier in this module we defined ‘Intrinsic Value’ as the money you are to receive, if you were to exercise your option today. Just to refresh your memory, let us calculate the intrinsic value for the following options assuming Nifty is at 8423 –

  1. 8350 CE
  2. 8450 CE
  3. 8400 PE
  4. 8450 PE

We know the intrinsic value is always a positive value or zero and can never be below zero. If the value turns out to be negative, then the intrinsic value is considered zero. We know for Call options the intrinsic value is “Spot Price – Strike Price” and for Put options it is “Strike Price – Spot Price”. Hence the intrinsic values for the above options are as follows –

  1. 8350 CE = 8423 – 8350 = +73
  2. 8450 CE = 8423 – 8450 = -ve value hence 0
  3. 8400 PE = 8400 – 8423 = -ve value hence 0
  4. 8450 PE = 8450 – 8423 = + 27

So given that we know how to calculate the intrinsic value of an option, let us attempt to decompose the premium and extract the time value and intrinsic value. Have a look at the following snapshot – Image 1 _IVTV Details to note are as follows –

  • Spot Value = 8531
  • Strike = 8600 CE
  • Status = OTM
  • Premium = 99.4
  • Today’s date = 6th July 2015
  • Expiry = 30th July 2015

Intrinsic value of a call option – Spot Price – Strike Price i.e 8531 – 8600 = 0 (since it’s a negative value) We know – Premium = Time value + Intrinsic value 99.4 = Time Value + 0 This implies Time value = 99.4! Do you see that? The market is willing to pay a premium of Rs.99.4/- for an option that has zero intrinsic value but ample time value! Recall time is money Here is snapshot of the same contract that I took the next day i.e 7th July – Image 3_IVTV Notice the underlying value has gone up slightly (8538) but the option premium has decreased quite a bit! Let’s decompose the premium into its intrinsic value and time value – Spot Price – Strike Price  i.e  8538 – 8600 = 0 (since it’s a negative value) We know – Premium = Time value + Intrinsic value 87.9 = Time Value + 0 This implies Time value = 87.9! Notice the overnight drop in premium value? We will soon understand why this happened. Note – In this example, the drop in premium value is 99.4 minus 87.9 = 11.5. This drop is attributable to drop in volatility and time. We will talk about volatility in the next chapter. For the sake of argument, if both volatility and spot were constant, the drop in premium would be completely attributable to the passage of time. I would suspect this drop would be around Rs.5 or so and not really Rs.11.5/-. Let us take another example – Image 2_ITVT

  • Spot Value = 8514.5
  • Strike = 8450 CE
  • Status = ITM
  • Premium = 160
  • Today’s date = 7th July 2015
  • Expiry = 30th July 2015

Intrinsic value of call option – Spot Price – Strike Price  i.e  8514.5 – 8450 = 64.5 We know – Premium = Time value + Intrinsic value 160 = Time Value + 64.5 This implies the Time value = 160 – 64.5 = 95.5 Hence out of the total premium of Rs.160, traders are paying 64.5 towards intrinsic value and 95.5 towards the time value. You can repeat the calculation for all options (both calls and puts) and decompose the premium into the Time value and intrinsic value.

14.2 – Movement of time

Time as we know moves in one direction. Keep the expiry date as the target time and think about the movement of time. Quite obviously as time progresses, the number of days for expiry gets lesser and lesser. Given this let me ask you this question – With roughly 18 trading days to expiry, traders are willing to pay as much as Rs.100/- towards time value, will they do the same if time to expiry was just 5 days? Obviously they would not right? With lesser time to expiry, traders will pay a much lesser value towards time. In fact here is a snap shot that I took from the earlier months – Image 4_Idea option chain

  • Date = 29th April
  • Expiry Date = 30th April
  • Time to expiry = 1 day
  • Strike = 190
  • Spot = 179.6
  • Premium = 30 Paisa
  • Intrinsic Value = 179.6 – 190 = 0 since it’s a negative value
  • Hence time value should be 30 paisa which equals the premium

With 1 day to expiry, traders are willing to pay a time value of just 30 paisa. However, if the time to expiry was 20 days or more the time value would probably be Rs.5 or Rs.8/-. The point that I’m trying to make here is this – with every passing day, as we get closer to the expiry day, the time to expiry becomes lesser and lesser. This means the option buyers will pay lesser and lesser towards time value. So if the option buyer pays Rs.10 as the time value today, tomorrow he would probably pay Rs.9.5/- as the time value. This leads us to a very important conclusion – “All other things being equal, an option is a depreciating asset. The option’s premium erodes daily and this is attributable to the passage of time”. Now the next logical question is – by how much would the premium decrease on a daily basis owing to the passage of time? Well, Theta the 3rd Option Greek helps us answer this question. M5-Ch14-Cartoon

14.3 – Theta

All options – both Calls and Puts lose value as the expiration approaches. The Theta or time decay factor is the rate at which an option loses value as time passes. Theta is expressed in points lost per day when all other conditions remain the same. Time runs in one direction, hence theta is always a positive number, however to remind traders it’s a loss in options value it is sometimes written as a negative number. A Theta of -0.5 indicates that the option premium will lose -0.5 points for every day that passes by. For example, if an option is trading at Rs.2.75/- with theta of -0.05 then it will trade at Rs.2.70/- the following day (provided other things are kept constant). A long option (option buyer) will always have a negative theta meaning all else equal, the option buyer will lose money on a day by day basis. A short option (option seller) will have a positive theta. Theta is a friendly Greek to the option seller. Remember the objective of the option seller is to retain the premium. Given that options loses value on a daily basis, the option seller can benefit by retaining the premium to the extent it loses value owing to time. For example if an option writer has sold options at Rs.54, with theta of 0.75, all else equal, the same option is likely to trade at – =0.75 * 3 = 2.25 = 54 – 2.25 = 51.75 Hence the seller can choose to close the option position on T+ 3 day by buying it back at Rs.51.75/- and profiting Rs.2.25 …and this is attributable to theta! Have a look at the graph below – Image 5_Time Decay This is the graph of how premium erodes as time to expiry approaches. This is also called the ‘Time Decay’ graph. We can observe the following from the graph –

  1. At the start of the series – when there are many days for expiry the option does not lose much value. For example when there were 120 days to expiry the option was trading at 350, however when there was 100 days to expiry, the option was trading at 300. Hence the effect of theta is low
  2. As we approach the expiry of the series – the effect of theta is high. Notice when there was 20 days to expiry the option was trading around 150, but when we approach towards expiry the drop in premium seems to accelerate (option value drops below 50).

So if you are selling options at the start of the series – you have the advantage of pocketing a large premium value (as the time value is very high) but do remember the fall in premium happens at a low rate. You can sell options closer to the expiry – you will get a lower premium but the drop in premium is high, which is advantageous to the options seller. Theta is a relatively straightforward and easy Greek to understand. We will revisit theta again when we will discuss cross dependencies of Greeks. But for now, if you have understood all that’s being discussed here you are good to go. We shall now move forward to understand the last and the most interesting Greek – Vega!


Key takeaways from this chapter

  1. Option sellers are always compensated for the time risk
  2. Premium = Intrinsic Value + Time Value
  3. All else equal, options lose money on a daily basis owing to Theta
  4. Time moves in a single direction hence Theta is a positive number
  5. Theta is a friendly Greek to option sellers
  6. When you short naked options at the start of the series you can pocket a large time value but the fall in premium owing to time is low
  7. When you short option close to expiry the premium is low (thanks to time value) but the fall in premium is rapid

161 comments

  1. Pankit Shah says:

    Nitinji,
    Its a bit confusing…so what u mean to say is :If i buy options at start of series,i would always lose money at the end of expiry due to theta…then when should one be a buyer of options?
    Also,according to u,what is more profitable…futures or options?

    • Karthik Rangappa says:

      Pankit – you missed one important line 🙂

      “All else equal then by virtue of time the premium value decreases on a daily basis”. But in reality “all else” is not equal. So on hand if theda decreases premium value, delta or vega will increase the premium value. So it it very important to understand all the greeks and its cross dependencies. We will talk about it later in this module.

  2. amit pathak says:

    Sir,
    Pls explain theta vs time for expiration w.r.t ITM,OTM & ATM options

  3. Sanatharam says:

    Whether theta will help in intraday trading if I short delta neutral deep OTM options..

  4. ramesh says:

    snapshot 2 and 3 are interchanged!

  5. R P HANS says:

    Sir,
    Again it is very simple and crisp explanation. Thanks.
    Is the theta value is same for all stocks keeping all other factors same? What u have shown is drop in the premium verses time. What will be the theta value verses time? I believe that it will change inversely and exponentially with time.
    Theta is friend for the seller is well understood, so if we sell a deep OTM option so that the probability of its expiring worthless is more and to pocket the premium at the expiry, may be a safe deal?

    • Karthik Rangappa says:

      Theta varies stock to stock, but certainly behaves the same for all stocks and indexes. In fact theta increases as we process in time…so less time to expiry, the more the theta, hence more the drop in premium, by virtue of time. You are absolutely bang on the money regarding OTM options.

      • Sumeet Nagar says:

        selling a deep OTM option is fine. But the question is will get the buyer for the deep OTM option?? I am novice in options. havent traded yet. Just aski

        • Sumeet Nagar says:

          selling a deep OTM option is fine. But the question is will get the buyer for the deep OTM option?? I am novice in options.,havent traded in options yet. Just asking based on ur experience..

        • Karthik Rangappa says:

          You do, at least in Nifty and few stocks.

  6. khyati verdhan says:

    Hi kartik,
    Thanks for this wonderful chapter. In one reading I almost understand the concept of chapter. it’s contents are very clear and easy.
    Everyday I closes my position my position before 3:20 p.m. so I think theta will not effect my trade as decline in price occurs on everyday basis. Please correct if am wrong.

    • Karthik Rangappa says:

      Theta does not play a big role when it comes to intraday trading. However the effect of theta is high just around expiry…so please be aware of this.

  7. R P HANS says:

    Intrinsic value of call option –

    Spot Price – Strike Price i.e 8514.5 – 8450 = 64.5 (since it’s a negative value)
    In the above text I think the “(since it’s a negative value)” is a copy and paste error. as the IV is 64.5 a non zero value. Please clarify.
    Thanks

  8. Saurabh says:

    Karthik my question is:

    Say I am an option seller (S1) who sells 1 contract of an OTM CE for 90 to an option buyer (B1). Three days later the option is still OTM and the premium drops to 80. Now If I square off my position. This means I am essentially closing the trade and transferring the risk of selling the option to somebody else (S2) with a profit of Rs.10. Let us say the person who bought the contract (B1) for 90 still holds it:

    In this case:

    1. S1 initially received Rs.90 from B1
    2. Three days later S1 closed the position and the contract was automatically transferred to S2 for a premium of Rs.80

    Now say the option becomes ITM and costs Rs. 120 on day 4 and buyer B1 closes his position and the contract gets transferred to B2.

    In such cases where people square off on the basis of premium changes – who is the final owner and which seller finally pays if the premium rises? Would S1 be involved or would S2 pay for the premium rise from 80 to 120 to B1?

    • Karthik Rangappa says:

      Saurabh – your thought process is correct, in fact most of the option trading is a play on premiums. In fact this point will strongly emerge towards the end of the module. The final owner and the seller will the those who hold on to the contract on the settlement day. So for example Nifty 8400 contract can be bought and sold by many traders during expiry…but the final set of traders who own (either bought or sold) matter for settlement.

      Hope I’m not confusing you with that 🙂

  9. Amarjeet Singh says:

    Mistake at chapter 14.3:
    A Theta of -0.5 indicates that the option premium will lose -0.5 points for every day that passes by. For example, if an option is trading at Rs.2.75/- with theta of -0.5 then it will trade at Rs.2.70/- the following day (provided other things are kept constant).
    ACTUALLY THE NEXT DAY OPTIONS VALUE SHOULD BE 2.25 AND NOT 2.70
    PLEASE RECTIFY THIS.

  10. Mukul says:

    HI Karthik,
    How I can check theoretical value calculation of Call/Put options ,which give the exact value of Gamma/Delta/Theta

  11. Abhijit Haware says:

    Hello Karthik….
    Thanks for info on theta….eagerly waiting for next chapters…

  12. Jagadeesh says:

    Thanks for the article Sir… 🙂

  13. Saurabh says:

    Karthik,

    I think it would be a good idea to consolidate all the important questions that add to the context of the different chapters and create a separate page for the same. And if possible then remove the comments asking for ‘when is the next one coming’ from the comments of the previous chapters. While it seems beneficial to me to see what other folks are asking as questions, it is difficult to find the relevant questions pertaining to the corresponding chapters due to the above reason.

    See if something can be done 🙂

  14. Vidhyalakshmi says:

    Hey Karthik, just saw your interview on MoneyControl.com. You should so have a discussion forum on Zerodha to discuss multibaggers, stock picks and the process of choosing multibaggers…the nitty gritties. It will be a valuable practical exercise in fundamentals for us.

    • Karthik Rangappa says:

      Hi Vidya, glad you bothered to watch 🙂

      Thanks for suggesting, may not be a bad idea. Will bounce this off internally 🙂

  15. R P HANS says:

    Today Sun Ph is up by around 3 rs to 949/- but its CE 1000 has gone down 25.40 to 23.10 and pe1000 has gone up 22.45 to 28..05. Why it is so, not able to understand. See the copy paste below.
    Previous LTP
    close
    30 Jul 2015 CE 1000.00 23.95 18.75 25.40 23.10 2518 6427.26 1040500 Jul 20 2015,11:32:00 AM
    30 Jul 2015 PE 1000.00 31.60 24.00 22.45 28.05 672 1728.10 285000 Jul 20 2015,11:32:00 AM
    Can you please explain this.
    Thanks.

    • Karthik Rangappa says:

      As I’ve mentioned – option prices are not just affected by directional movement but lot of other variables. In this particular case, 1000 CE is OTM and 100PE is ITM…remember ITM options are more sensitive to price changes.

  16. sarath says:

    we are waiting for the next chapter , when will it come?

  17. Arunram0330 says:

    Hi Karthik,
    All the chapters are very easy to understand and easy to relate with. I just have a small query. How to calculate the number of day to expiry. Do we need to add only the traded days or do need to add non traded days (Weekends) with traded days to get the total.

  18. Ajay says:

    Hey Karthik. The value of the premium = Intrinsic value + Time value. At any point, is it possible for Time value to be negative?

    • Ajay says:

      w.r.t the 7500 CE, the Premium is 790.7. This was as on Friday, where the spot was 8,299.95. So the intrinsic value is 799.95(8299.95-7500, which means the time value is -9.25(790.7-799.95)?

      • Karthik Rangappa says:

        8299.95 – 7500 = 799.95 (this is the intrinsic value and the minimum option premium). The premium is 790.7 (maybe because its not liquid, hence the mis pricing). Time value is 0 and not -ve.

    • Karthik Rangappa says:

      No, neither time value or intrinsic value can be -ve.

  19. Sunil Tyagi says:

    Karthik you are a great teacher this chapter is an example how a good teacher can make esoteric topics look simple.
    However, I feel the value of theta should be negative if it is taken as rate of change of premium with respect to time. It would be mathematically correct as well.

    • Karthik Rangappa says:

      Thanks for the kind words Sunil. Theta is a -ve value, as it indicates the fact that premiums lose value as time passes (assuming all else constant).

  20. Sucheta says:

    Hi Karthik,

    I am keeping mum with the awful simplicity of the material. Chapter by chapter I am grasping details and structure of the options. I had started to trade in options thinking that those are easy and straight forward like futures. However, my calculations went wrong at the time of expiry. I didn’t know all this background which I am referring. I cannot express my gratitude in words. You are great teacher. Keep imparting the knowledge. Thank you very much once again.

    • Karthik Rangappa says:

      Thank you and I really hope you find all the other modules/chapters equally good. All the best and please do stay tuned on Zerodha Varsity.

  21. jagdish says:

    how u control the operator who actually moves the LTP against ur all calculations,on increase of price he keeps the LTP not to change proportionally and u r put to loss what to do?

    • Karthik Rangappa says:

      As long as you deal with highly liquid stocks like HUl, ITC, Reliance, Infy, Nifty etc you need not worry about any operator.

  22. PRASHANTH AV says:

    IS THETA A CONSTANT GREEK OR VARIABLE LIKE DELTA AND GAMMA

  23. Shrenik Shah says:

    Assume that I sell a call option at 8700 Strike Price(Jan expiry option) on Jan 1st 2016 at a premium of 80Rs (OTM) . Somehow nifty keeps falling goes towards 8300 and by the end of the expiry it only recovers and closes at 8500. Does this mean, I will retain the whole premium because it will eventually drop to 0Rs?
    I am asking you because I want to know, if I am at thinking on the right path? Assuming the other thing remains constant.

    • Karthik Rangappa says:

      Absolutely. 8700 CE will be In the Money only if upon expiry the spot is higher than the Strike. If the spot is lesser (like 8500 or so) then the option will not have any intrinsic value hence you get to retain the entire premium of Rs.80.

  24. rohan says:

    wipro
    spot-559
    strike-580

    580CE
    Premium-5.75
    delta=.401,gamma-=0079,theta=-.207
    if spot moves 10 points in 10 days the-
    new premium= 5.75 + 10(.401) + 10(-.207)=9.76-2.07=7.69

    if spot moves -10
    new premium=5.75 -10(.401) -10(-.207)= 1.74 +2.07 = 3.81

    my questions-
    a) are my calculations of new premium correct?
    b) when spot is moving down in call option theta is adding to premium . as spot =-10 and theta=-.207 so minus multiply by minus becomes plus.But it should not be the case as premium should decrease??

    • Karthik Rangappa says:

      You also need to take into account Volatility (vega) which calculating new premium, but assuming volatility is constant your calculations are ok. Do remember, Theta always tend to eat away the premiums (hence good for option writers).

      • jitu says:

        Sir, please provide option calculator as well as value of all Greeks at kite in live market that uses volatility from India vix. It will be very helpful to trader , at least for nifty and Bank Nifty.

  25. rohan says:

    Thanks Kathik….

    In my previous calculations, I think there is some error in second one when spot goes down by -10
    new premium=5.75 -10(.401) -10(-.207)= 1.74 +2.07 = 3.81

    here premium is increasing with theta(-10*-.207=+2.07)

    how come?

    • Karthik Rangappa says:

      Here is the general framework Rohan – For a call option with increase in spot price/time/volatility, the delta increases hence adds to premium, time value decreases hence drags down the premium, and with increase in vega the premium increases.

      For a put option with decrease in spot price/volatility, the delta increases hence adds to premium, with increase in vega the premium increases. Time moves in only 1 direction hence it always tends to drag the premium lower.

      • RS6006 says:

        Can you explain how decrease in volatility increases the delta of a put option. I am of the opinion, decrease in volatility decreases the option premium of either put/call option.

        • Karthik Rangappa says:

          Can you please share the link where I’ve mentioned this? Yes, volatility and premium are linearly related.

          • RS6006 says:

            In the above comment to Rohan you mentioned “For a put option with decrease in spot price/volatility, the delta increases hence adds to premium, with increase in vega the premium increases. Time moves in only 1 direction hence it always tends to drag the premium lower.”

          • Karthik Rangappa says:

            I stand corrected, it should read “For a put option with decrease in spot price, the delta increases hence adds to premium…..”

  26. SONJOE JOSEPH says:

    Dear Sir,

    Using the black scholes model what’s the formula for calculating the Delta, Gamma, Theta, Vega and Rho. Even at zerodha site there is a Black scholes calculater were i have found the values of Delta, Gamma, Theta, Vega & Rho. How have u arrived at this values. Just need the formula to calculate it in excel.

    Sonjoe Joseph

  27. garg10may says:

    Does Theta play a role when I buy say after 3:00 and sell tomorrow. Or it decays over the day?

  28. garg10may says:

    How can I pull the values of greeks in Pi, I remember this was available in Nest Trader. You could also provide the same in kite, maybe a separate page also support for entering option leg orders..

  29. deepak dhanwani says:

    Dear karthik sir,
    I have a question….assume that i am selling 8500ce @ 20rs. And spot is 8200 before 5 days of expiry and on expiry day nifty comes upto 8450 spot and premium becomes 30rs somehow…so still 8500ce is otm…so will get 30rs. Premium as profit or 20-30=10rs. Loss ???

    • Karthik Rangappa says:

      If the expiry happens at 8450, then you will still get to retain the Rs.20 as profits. However if spot closes at 8510, then you will lose Rs.10…and if spot closes at 8520, you will not make anything…and anything above 8520 is a loss for you.

  30. Raj says:

    “Time moves in a single direction hence Theta is a positive number.”
    “Theta is a friendly Greek to option sellers.”
    I can’t relate any point here. Being Theta +ve, why do we take -ve value for Theta in a long position to calculate premium depending upon expiry.
    You have shown examples while selling option. Can you please elaborate the same with a buying option as
    1. Buying Call; Market is rising and Days are expiring, but the premium is rising.
    2. Buying Put; Market is falling and Days are expiring, but the premium is rising

    • Karthik Rangappa says:

      Example : Theta of +0.2 implies that the premium erodes 0.2 points on a daily basis till we hit expiry…this is assuming all else equal.

      1 & 2) This is because of increase in delta or maybe volatility. The same explanation holds true for both the cases you mentioned.

  31. punit417 says:

    Dear Sir,

    How can time value for a call option be negative when there are still 2 weeks left for expiry? Please see below example I took from NSE website today, i.e. 12th Aug 2016:

    Spot price – 365.55
    Option type – Call option
    Strike price – 320 (ITM)
    Premium price (Call Option) – 29.5

    Derived Intrinsic value = 365.55 – 320 = 45.55
    Time risk value of option = Premium minus Intrinsic value = 29.5 – 45.55 = (16.05)

    Please explain the rationality of such premium pricing. Can there be any trading opportunity in above?

    Thanks

    • Karthik Rangappa says:

      This is because options are considered a depreciating asset and it depreciates with the passage of time as time moves only in one direction.

      • punit417 says:

        Thanks sir for the reply.
        Does that mean that time value of the option can go negative even if there are two weeks left for expiry? My understanding is that time value of an option will depreciate towards zero(it should not go below zero) as expiry time approaches.

        Please clear my understanding.
        Thanks a lot in advance.

        • Karthik Rangappa says:

          Yes, TV depreciates from a positive value all the way to 0 in such a way that it coincides to 0 on the day of expiry (at 3:30PM).

  32. punit417 says:

    Thanks for the reply. So under what conditions, time value can go negative before the expiry?

    Thanks a lot on advance.

    • Karthik Rangappa says:

      Cant really go to -ve. It terminates at 0.

      • punit417 says:

        Thanks. But in the example above, I have shown the calculation that time value is negative for a call option. Kindly explain how is that possible. Data is taken from NSE website.

        • Karthik Rangappa says:

          The -ve sign just indicates that the value is a depreciating one. Think about it, options expire on expiry day…given this the least the TV can go is 0 because on expiry day the contract ceases to exist.

  33. Rishikesh says:

    Hi Karthik,

    As mentioned in the chapter , the Intrinsic value can never be zero.
    For a call CE option the Intrinsic Value (IV) is calculated as “Spot price – Strike price”.

    But if we see on the option chain of Ashok Leyland on the link

    https://www.nseindia.com/live_market/dynaContent/live_watch/option_chain/optionKeys.jsp?symbolCode=228&symbol=ASHOKLEY&symbol=ASHOKLEY&instrument=-&date=-&segmentLink=17&symbolCount=2&segmentLink=17

    the IV column has some high numbers which are not “Spot price – Strike price”.

    Can you please let me know what these numbers are in IV column?

    Thanks,
    Rishikesh

    • Karthik Rangappa says:

      The intrinsic value can never be below zero….however, it can be zero. The IV that you see in the option chain is ‘Implied Volatility’ and not the intrinsic value 🙂

  34. Abhijit says:

    Hey Karthik,

    You said an option is depreciating asset and premium erodes daily. I can understand this for call option where strike price is greater than spot price. But what about when strike price is lower than spot price already? i.e. ITM
    Spot – 8000
    Strike – 7700
    Premium – 100

    Wouldn’t premium will increase in this case as time passes? Call seller is almost certain to lose premium.

    • Karthik Rangappa says:

      If spot is at 8000 then the premium for 7700 CE would be at least 300. If there is ample time to expiry..then the premium will be more than 300…if nothing else changes, then the portion over and above 300 will erode as time passes. This is mainly attributable to time decay.

  35. Deepesh Yadav says:

    Hi Karthik,
    Hope you are doing great!
    I am a newbie in markets and after reading this i started fantasying about making money buy selling both call and put for a strike price. Assuming that there wont be any effect of directional movement on this kind of position, As time will pass (let say a week) the total value of the option will decrease due to time decay and we can lock in the profits by buying them. is it feasible or i am missing something because everyone can think of this strategy. Please enlighten me on this. Thank you

  36. Ankit says:

    Hi karthik sir
    Sir what is RHO is this also a topic in this module

    • Karthik Rangappa says:

      Rho is an option greek which measures the sensitivity of the premium with respect to change in interest rate. Since interest rates dont change often, we have just omitted this greek.

  37. Ankit says:

    Thanks for clarification

  38. adityasingh says:

    Sir, minimum sip in most of mf is 5000, i wanted to start with 1000 in kotak select focus, is their any way ?

  39. Ankit says:

    Sir,
    Sir is ITM and OTM contains little time value if yes
    Then is there a way how to calculate that time value
    Simply i want to ask how to seperate ITM’s time value and intrinsic value

  40. Ankit says:

    Hello sir,
    I tried it but did not get results
    Ex:- For Otm (CE)options if premium is at 8 then, as per formula
    Time value =premium-intrinsic value
    Since,intrinsic value is 0 for OTM so, all the premium is for time value
    BUT in case of ITM option where premium contains Non zero number for
    both Intrinsic and time Premium not maching with formula i saw in many strikes the ITM’s time value coming in MINUS NUMBER
    EX:-
    PREMIUM= Intrinsic+time
    35=40(int value) + time value
    Time value =35-40 =-5
    what this suggests is premium drop for time is more than is should be???????

    • Karthik Rangappa says:

      ITM options contains high Int value and low time value. I’m a little confused on what you are trying to calculated. Can you please explain this again for me, please. Thanks.

  41. Ankit says:

    Okay sir,
    Take this example(imagined not real) of CALL OPTION
    Spot 400
    Strike 370
    9 days to expiry
    Status – DEEP ITM
    Premium 25
    Sir my question is if we playing a ITM OPTION
    Then that option must have positive intrinsic value and positive time value
    Say atlest 5 or 7 or 10 or whatever you say for time value
    Intrinsic value = spot-strike=400-370=30 right
    Then premium must be more than 30 for above case
    But instead of >30 it is at 25
    This driving me to this formula
    Premium = (spot-strike)+time value
    25=(400-370)+time value
    Time value= 25-30=-5
    Is this suggests the time value is in minus (i think not possible)
    Premium must have ZERO or a positive mon ZERO NUMBER FOR both its content.
    Sir this is really happend i was considering a stock option few days ago
    Where ITM option premium was different from what we have knows…….
    Thanks sir…..

    • Karthik Rangappa says:

      In the example quoted above, the option price must be at least 30 (int value). Anything lesser than that is an aberration and will get sucked up by the markets soon. Its highly unlikely that you will come across such situations. If you do, you need to buy the option and wait for the premium prices to reflect the right price.

  42. Ankit says:

    Hi karthik sir,
    I want your opinion here. What do you say about STRIKE VS TIME VALUE
    For an ATM option the time value’s share in premium is maximum and we move to ITM from ATM or to OTM from ATM. The time value starts decreasing and forms a chart like gama (the bell looking) chart
    i always thinks that we should not buy optiïon when there is just 10 to 14 days left in expiry because in normal days the movement in underlying stays close to its AVERAGE and THETA beats the DELTA and you always end with lose due to theta
    But now with this BELL curve of time value vs strike we can consider buying in ITM and OTM if we have predicted that underlying will move in a meaning full manner and with this we can expect almost same gain as in starting of series where theta is lowest
    I mean in above case the decrease is premium will be lower due to THETA campare to increasing in premium due to DELTA if there is noticiable DELTA
    if i am doing this trade i wil get out of the trde before expiry for OTM as it has to be ZERO at expiry
    So, what do you say is this right thing to do….??????

    • Karthik Rangappa says:

      Yes, you can. In fact, when you are convinced about the directional movement, the best option always is to buy options….especially when you also have time working in your favor. Also remember, the effect of Theta starts to forcefully kick in towards the end of the series….maybe when there are 5 days to expiry or last week of expiry. Take up the trade if you are convinced, but square off before expiry.

  43. SHRI KRISHAN GUPTA says:

    Dear Karthik
    I was looking into NIFTY Option chain on 15.05.2017 for CE @stricke price of 8600 at a premium of 846.55 with NIFT spot at 9456.15. It indicates intrinsic value of 856.15 and hence a time value of -9.6. Is it possible. The expiry month is near month.

    • Karthik Rangappa says:

      Time value here is almost zero. Also, remember trades in deep ITM or OTM option will be few, hence liquidity is lesser, and therefore the premiums may not be priced right.

  44. SHRI KRISHAN GUPTA says:

    Dear Karthik
    Thanks for the guidance . Pls clarify my one more doubt:
    How is intrinsic value related to delta. Does it follow the same pattern as premium vs delta.

    • Karthik Rangappa says:

      Delta is one of the forces which has an impact on IV along with other greeks like vega, theta, and gamma.

  45. SHRI KRISHAN GUPTA says:

    Dear karthika
    Thanks for your guidance that helped me to pick up the nitty-gritty of Options.Please clarify my following doubts:
    1.If I shift my broker to zerodha will my current holdings be transferred. If yes what is the method.
    2. Since OTM options have IV of zero, and delta affects only IV , so how does delta really affects an OTM option.

  46. Ravi says:

    Hi Karthik

    As mentioned above due to time decay premium decrease, but using Black and Schole Calc I found that for Deep ITM, PUT premium increases with time decay as the theta is +ve for deep ITM? How is it possible??

    Can you Please explain. It means if we go long on Deep ITM Put then time decay will favour Long postions considering market remains static(value doesn’t change)??

    • Karthik Rangappa says:

      In general theta has a -ve effect on options premium. However, yes, deep ITMs premium do tend increase as the probability of deep ITM remaining ITM increases as time to expiry decreases. This can however, be attributed to deeper deltas.

  47. James says:

    Respected Sir,
    Keeping all else constant, when does Theta effect take place? Does premiums gradually decline during the trading session, or does the next day trading session open directly after specific deductions (equal to theta value) in premium prices, or both?
    Thanks in advance !!!
    Best Regards
    James

    • Karthik Rangappa says:

      The effect of theta starts from the time a contract comes into existence. However, the effect is not really felt by traders when the contract is young and early in the cycle. However, as the contract ages and approaches expiry, theta accelerates and the effect intensifies.

      • James says:

        Sorry! I guess I couldn’t make myself clear. I am new to option trading so curious about theta decay while market is closed. For example, option premium of XYZ on Monday was-
        Open-11.20,
        High – 14.27,
        Low – 7.42,
        Close – 8.42
        Of course, theta contributed to drop in price from 14.27 to 7.42 during the Monday session. But,
        Q.) What will be open price of premium on Tuesday (assuming all other factors remain same)? Will it be 8.42 (Monday’s close) or something less due to theta effect?
        Thanks & Regards
        James

        • Karthik Rangappa says:

          Theta could not have contributed to a drop from 14.27 to 7.42 – clearly delta is playing the prank here.

          If the theta is 0.5, then all else equal, the premium will trade 0.5 less of 7.42.

  48. ANU says:

    Hi,
    All your modules are very informative! Kudos for this yet another initiative from zerodha!
    I had one query regarding greeks I sold one lot of stock option on 27th Jun strike price was 740 and spot was 670! The premium recieved was 8.30 !
    Today the spot is 745 and the premium is around 13!
    1) Is it correct that my breakeven on expiry will be 748.3 (spot)
    2) Would I recieve a higher premium if I would have sold the same stock option say strike price 750 today 4 days from expiry?
    Thanks!

  49. anu says:

    Completed the first 10 chapters of this module..I have never found anything on options trading to be this simple and precisely explained before..hats off to you Sir..
    Wishing you and your team the best of luck!!

  50. ayas says:

    sir, i am confused
    there should be increase in premium with increase in underlying,
    suppose;
    i am long on CE and the underlying price moves up in my favor and now i want to sqaureoff my position next day, what will happen?
    will i lose money because of dercease in premium?

    • Karthik Rangappa says:

      For long positions, as long as the premium is above your buy price you will make money. Likewise, when you sell (write) options as long as the premium is below your sell price you will profit.

  51. rahul says:

    Karthik,

    Just a suggestion on page navigation:

    Its fairly easy to navigate to a different chapter in a module if I start reading from the top. However, its extremely difficult to get to module-navigation from bottom; one has to keep scrolling / pg-up repeatedly. This gets bothersome if you’re trying to jump across different chapters / refresh your concepts that you can’t recall etc.

    I’d like to suggest adding links at the very top + very bottom (right above the comment box) of the page to the table-of-contents for ease of navigation.

    Great stuff! Keep up the good work.

  52. NAJEEB says:

    Hi Kartik

    Sorry for taking the query regarding theta in the volatility group .What will be the percentage decay of the option on a daily basis daily supposing the underlying stays at at the money(theoretical) till the life of the option .Also is there any relation in percentage between daily volatility and theta percentage when underlying at the money? For eg if there were 20 days to expiry and at the money premium is 20 what will be the percentage decay on a daily basis.Will it be eroding the same percentage on a daily basis or rapid erosion on expiry and if not uniform the difference in percentage?

    • Karthik Rangappa says:

      No problem, Najeeb. I answered it there as well.

      If all else equal, the loss in option premium owing to time decay is equivalent to the theta of the option.

      If the volatility increases, then the premiums also tend to increase. This is especially true when there us fewer days to expiry.

  53. Sashidhar. L says:

    Sir after reading this chapter I checked out few of the charts and what I observed was that option premium has the highest value at the start of the contract (I’m guessing due to time) and gradually decrease in value over time. So am I right in saying that if you are the option seller at the beginning of the contract you are always on the right side?

    • Karthik Rangappa says:

      I’d agree, however, if during the series the stock/index gains a lot of momentum then you could be in trouble doing this.

  54. Razin says:

    Is there any video blog for the same?

  55. Azeem says:

    Spot nifty 10760
    I Buy Nifty CE 10750
    Delta = 0.55 Premium = 131 Theta = 5.00
    Premium = Int value + time value
    = 10 + 121
    All other things remaining constant, will the premium drop by 5 rs to 126 rs the next day ?

  56. Azeem says:

    Nifty Spot = 10760
    CE 10850 Premium = 83
    CE 10900 premium = 65
    Both intrinsic value is 0 but time value has a difference of 18 rs. How to arrive at this 83 and 65 rs time value ?
    So like delta of atm options is always around 0.5 what is the formula for calculating time value ?

  57. Vidya says:

    Dude, you are God! Love your teaching skills. Thank you so much for all this effort that you have put and continue to put into the teaching. Greatly appreciate your work.
    Vidya

  58. Prakhar says:

    Does rate of premium on Friday 3:25pm be discounted for the two days theta decay.

  59. mahesh says:

    Thanks for lucid explanation.

    Does theta changes w.r.t underlying spot price like delta or is it fixed?

  60. Patki says:

    Dear Karthik,
    Say I have sold OTM Strike price Bank Nifty and its value becomes zero on expiry and remains OTM. Before it expires shall I have to buy the contract to complete the transaction or allow it to lapse at zero. What about the brokerage and tax and will the profit b credited to my a/c even though I allowed it to expire? Pl. Clarify

    • Karthik Rangappa says:

      Yes, you can let the option expire worthlessly. No problem with it. You will get to retain the entire premium.

  61. Shicansh says:

    If i sold deep otm put and it expires as otm then i will get the entire premium right??

  62. SHyam says:

    this is the most easiest greek 🙂

  63. Chirag Sharma says:

    Spot Price: 10630
    Strike Price: 10700
    Premium: 2.8
    Delta: assuming 0.2( since it’s OTM)

    Now next day, big jump
    Spot Price: 10730
    Strike: 10700
    Premium: (10730-10630)*0.20+2.8= 22.8

    Question:
    Since the premium is 22.8 and Intrinsic value is 30(10730-10700), is the whole premium attributable to intrinsic value and nothing to time value?

  64. Mayursinh shinol says:

    I think premium should be sum of intrinsic value and extrinsic value(implied volatility + Time value)..You just stated time value and ignored Implied volatility..If Implied volatility increases it will definetely increase premium..

    • Karthik Rangappa says:

      Mayursinh, when we say time value, it includes implied volatility. Remember, implied volatility is one of the parameters of time value…or in other words, time value is a function of time to expiry, IV, Strike, and the option type. Most traders think time value is just attributable to time to expiry, in a sense its true, but it also includes other parameters.

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