Module 5   Options Theory for Professional TradingChapter 3

Buying a Call Option

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3.1 – Buying call option

In the previous chapters we looked at the basic structure of a call option and understood the broad context under which it makes sense to buy a call option. In this chapter, we will formally structure our thoughts on the call option and get a firm understanding on both buying and selling of the call option. Before we move ahead any further in this chapter, here is a quick recap of what we learnt in the first chapter –

  1. It makes sense to be a buyer of a call option when you expect the underlying price to increase
  2. If the underlying price remains flat or goes down then the buyer of the call option loses money
  3. The money the buyer of the call option would lose is equivalent to the premium (agreement fees) the buyer pays to the seller/writer of the call option

We will keep the above three points in perspective (which serves as basic guidelines) and understand the call option to a greater extent.

3.2 – Building a case for a call option

There are many situations in the market that warrants the purchase of a call option. Here is one that I just discovered while writing this chapter, thought the example would fit well in the context of our discussions. Have a look at the chart below –

Image-1_Bajaj-Auto-stock-price

The stock in consideration is Bajaj Auto Limited. As you may know, they are one of the biggest manufacturers of two wheelers in India. For various reasons the stock has been beaten down in the market, so much so that the stock is trading at its 52 week low price. I believe there could be an opportunity to initiate a trade here. Here are my thoughts with respect to this trade –

  1. Bajaj Auto is a quality fundamental stock, there is no denying this.
  2. The stock has been beaten down so heavily, makes me believe this could be the market’s over reaction to volatility in Bajaj Auto’s business cycle.
  3. I expect the stock price to stop falling sometime soon and eventually rise.
  4. However I do not want to buy the stock for delivery (yet) as I’m worried about a further decline of the stock.
  5. Extending the above point, the worry of M2M losses prevents me from buying Bajaj Auto’s futures as well.
  6. At the same time I don’t want to miss an opportunity of a sharp reversal in the stock price.

To sum up, I’m optimistic on the stock price of Bajaj Auto (the stock price to eventually increase) but I’m kind of uncertain about the immediate outlook on the stock. The uncertainty is mainly due the fact that my losses in the short term could be intense if the weakness in the stock persists. However as per my estimate the probability of the loss is low, but nevertheless the probability still exists. So what should I do?

Now, if you realize I’m in a similar dilemma that was Ajay was in (recall the Ajay – Venu example from chapter 1). A circumstance such as this, builds up for a classic case of an options trade.

In the context of my dilemma, clearly buying a call option on Bajaj Auto makes sense for reasons I will explain shortly. Here is a snapshot of Bajaj Auto’s option chain –

Image-2_Bajaj-Auto

As we can see the stock is trading at Rs.2026.9 (highlighted in blue). I will choose to buy 2050 strike call option by paying a premium of Rs.6.35/- (highlighted in red box and red arrow). You may be wondering on what basis I choose the 2050 strike price when in fact there are so many different strike prices available (highlighted in green)?. Well, the process of strike price selection is a vast topic on its own, we will eventually get there in this module, but for now let us just believe 2050 is the right strike price to trade.

3.3 – Intrinsic value of a call option (upon expiry)

So what happens to the call option now considering the expiry is 15 days away? Well, broadly speaking there are three possible scenarios which I suppose you are familiar with by now –

Scenario 1 – The stock price goes above the strike price, say 2080

Scenario 2 – The stock price goes below the strike price, say 2030

Scenario 3 – The stock price stays at 2050

The above 3 scenarios are very similar to the ones we had looked at in chapter 1, hence I will also assume that you are familiar with the P&L calculation at the specific value of the spot in the  given scenarios above (if not, I would suggest you read through Chapter 1 again).

The idea I’m interested in exploring now is this –

  1. You will agree there are only 3 broad scenarios under which the price movement of Bajaj Auto can be classified (upon expiry) i.e. the price either increases, decreases, or stays flat
  2. But what about all the different prices in between? For example if as per Scenario 1 the price is considered to be at 2080 which is above the strike of 2050. What about other strike prices such as 2055, 2060, 2065, 2070 etc? Can we generalize anything here with respect to the P&L?
  3. In scenario 2, the price is considered to be at 2030 which is below the strike of 2050. What about other strike prices such as 2045, 2040, 2035 etc? Can we generalize anything here with respect to the P&L?

What would happen to the P&L at various possible prices of spot (upon expiry) – I would like to call these points as the “Possible values of the spot on expiry” and sort of generalize the P&L understanding of the call option.

In order to do this, I would like to first talk about (in part and not the full concept) the idea of the ‘intrinsic value of the option upon expiry’.

The intrinsic value (IV) of the option upon expiry (specifically a call option for now) is defined as the non – negative value which the option buyer is entitled to if he were to exercise the call option. In simple words ask yourself (assuming you are the buyer of a call option) how much money you would receive upon expiry, if the call option you hold is profitable. Mathematically it is defined as –

IV = Spot Price – Strike Price

So if Bajaj Auto on the day of expiry is trading at 2068 (in the spot market) the 2050 Call option’s intrinsic value would be –

= 2068 – 2050

= 18

Likewise, if Bajaj Auto is trading at 2025 on the expiry day the intrinsic value of the option would be –

= 2025 – 2050

= -25

But remember, IV of an option (irrespective of a call or put) is a non negative number; hence we leave the IV at 2025

= 0

Now our objective is to keep the idea of intrinsic value of the option in perspective, and to identify how much money I will make at every possible expiry value of Bajaj Auto and in the process make some generalizations on the call option buyer’s P&L.

3.4 – Generalizing the P&L for a call option buyer

Now keeping the concept of intrinsic value of an option at the back of our mind, let us work towards building a table which would help us identify how much money, I as the buyer of Bajaj Auto’s 2050 call option would make under the various possible spot value changes of Bajaj Auto (in spot market) on expiry. Do remember the premium paid for this option is Rs 6.35/–. Irrespective of how the spot value changes, the fact that I have paid Rs.6.35/- remains unchanged. This is the cost that I have incurred in order to buy the 2050 Call Option. Let us keep this in perspective and work out the P&L table –

Please note – the negative sign before the premium paid represents a cash out flow from my trading account.

Serial No. Possible values of spot Premium Paid Intrinsic Value (IV) P&L (IV + Premium)
01 1990 (-) 6.35 1990 – 2050 = 0 = 0 + (– 6.35) = – 6.35
02 2000 (-) 6.35 2000 – 2050 = 0 = 0 + (– 6.35) = – 6.35
03 2010 (-) 6.35 2010 – 2050 = 0 = 0 + (– 6.35) = – 6.35
04 2020 (-) 6.35 2020 – 2050 = 0 = 0 + (– 6.35) = – 6.35
05 2030 (-) 6.35 2030 – 2050 = 0 = 0 + (– 6.35) = – 6.35
06 2040 (-) 6.35 2040 – 2050 = 0 = 0 + (– 6.35) = – 6.35
07 2050 (-) 6.35 2050 – 2050 = 0 = 0 + (– 6.35) = – 6.35
08 2060 (-) 6.35 2060 – 2050 = 10 = 10 +(-6.35) = + 3.65
09 2070 (-) 6.35 2070 – 2050 = 20 = 20 +(-6.35) = + 13.65
10 2080 (-) 6.35 2080 – 2050 = 30 = 30 +(-6.35) = + 23.65
11 2090 (-) 6.35 2090 – 2050 = 40 = 40 +(-6.35) = + 33.65
12 2100 (-) 6.35 2100 – 2050 = 50 = 50 +(-6.35) = + 43.65

So what do you observe? The table above throws out 2 strong observations –

  1. Even if the price of Bajaj Auto goes down (below the strike price of 2050), the maximum loss seems to be just Rs.6.35/-
    1. Generalization 1 – For a call option buyer a loss occurs when the spot price moves below the strike price. However the loss to the call option buyer is restricted to the extent of the premium he has paid
  2. The profit from this call option seems to increase exponentially as and when Bajaj Auto starts to move above the strike price of 2050
    1. Generalization 2 – The call option becomes profitable as and when the spot price moves over and above the strike price. The higher the spot price goes from the strike price, the higher the profit.
  3. From the above 2 generalizations it is fair for us to say that the buyer of the call option has a limited risk and a potential to make an unlimited profit.

Here is a general formula that tells you the Call option P&L for a given spot price –

P&L = Max [0, (Spot Price – Strike Price)] – Premium Paid

Going by the above formula, let’s evaluate the P&L for a few possible spot values on expiry –

  1. 2023
  2. 2072
  3. 2055

The solution is as follows –

@2023

= Max [0, (2023 – 2050)] – 6.35

= Max [0, (-27)] – 6.35

= 0 – 6.35

= – 6.35

The answer is in line with Generalization 1 (loss restricted to the extent of premium paid).

@2072

= Max [0, (2072 – 2050)] – 6.35

= Max [0, (+22)] – 6.35

= 22 – 6.35

= +15.65

The answer is in line with Generalization 2 (Call option gets profitable as and when the spot price moves over and above the strike price).

@2055

= Max [0, (2055 – 2050)] – 6.35

= Max [0, (+5)] – 6.35

= 5 – 6.35

= -1.35

So, here is a tricky situation, the result what we obtained here is against the 2nd generalization. Despite the spot price being above the strike price, the trade is resulting in a loss! Why is this so? Also if you observe the loss is much lesser than the maximum loss of Rs.6.35/-, it is in fact just Rs.1.35/-. To understand why this is happening we should diligently inspect the P&L behavior around the spot value which is slightly above the strike price (2050 in this case).

Serial No. Possible values of spot Premium Paid Intrinsic Value (IV) P&L (IV + Premium)
01 2050 (-) 6.35 2050 – 2050 = 0 = 0 + (– 6.35) = – 6.35
02 2051 (-) 6.35 2051 – 2050 = 1 = 1 + (– 6.35) = – 5.35
03 2052 (-) 6.35 2052 – 2050 = 2 = 2 + (– 6.35) = – 4.35
04 2053 (-) 6.35 2053 – 2050 = 3 = 3 + (– 6.35) = – 3.35
05 2054 (-) 6.35 2054 – 2050 = 4 = 4 + (– 6.35) = – 2.35
06 2055 (-) 6.35 2055 – 2050 = 5 = 5 + (– 6.35) = – 1.35
07 2056 (-) 6.35 2056 – 2050 = 6 = 6 + (– 6.35) = – 0.35
08 2057 (-) 6.35 2057 – 2050 = 7 = 7 +(- 6.35) = + 0.65
09 2058 (-) 6.35 2058 – 2050 = 8 = 8 +(- 6.35) = + 1.65
10 2059 (-) 6.35 2059 – 2050 = 9 = 9 +(- 6.35) = + 2.65

As you notice from the table above, the buyer suffers a maximum loss (Rs. 6.35 in this case) till the spot price is equal to the strike price. However, when the spot price starts to move above the strike price, the loss starts to minimize. The losses keep getting minimized till a point where the trade neither results in a profit or a loss. This is called the breakeven point.

The formula to identify the breakeven point for any call option is –

B.E = Strike Price + Premium Paid

For the Bajaj Auto example, the ‘Break Even’ point is –

= 2050 + 6.35

= 2056.35

In fact let us find out find out the P&L at the breakeven point

= Max [0, (2056.35 – 2050)] – 6.35

= Max [0, (+6.35)] – 6.35

= +6.35 – 6.35

= 0

As you can see, at the breakeven point we neither make money nor lose money. In other words, if the call option has to be profitable it not only has to move above the strike price but it has to move above the breakeven point.

M5-Ch3-title

3.5 – Call option buyer’s payoff

So far we have understood a few very important features with respect to a call option buyer’s payoff; I will reiterate the same –

  1. The maximum loss the buyer of a call option experiences is, to the extent of the premium paid. The buyer experiences a loss as long as the spot price is below the strike price
  2. The call option buyer has the potential to realize unlimited profits provided the spot price moves higher than the strike price
  3. Though the call option is supposed to make a profit when the spot price moves above the strike price, the call option buyer first needs to recover the premium he has paid
  4. The point at which the call option buyer completely recovers the premium he has paid is called the breakeven point
  5. The call option buyer truly starts making a profit only beyond the breakeven point (which naturally is above the strike price)

Interestingly, all these points can be visualized if we plot the chart of the P&L. Here is the P&L chart of Bajaj Auto’s Call Option trade –

Image-3_Payoff

From the chart above you can notice the following points which are in line with the discussion we have just had –

  1. The loss is restricted to Rs.6.35/- as long as the spot price is trading at any price below the strike of 2050
  2. From 2050 to 2056.35 (breakeven price) we can see the losses getting minimized
  3. At 2056.35 we can see that there is neither a profit nor a loss
  4. Above 2056.35 the call option starts making money. In fact the slope of the P&L line clearly indicates that the profits start increasing exponentially as and when the spot value moves away from the strike

Again, from the graph one thing is very evident – A call option buyer has a limited risk but unlimited profit potential. And with this I hope you are now clear with the call option from the buyer’s perspective. In the next chapter we will look into the Call Option from the seller’s perspective.


Key takeaways from this chapter

  1. It makes sense to be a buyer of a call option when you expect the underlying price to increase
  2. If the underlying price remains flat or goes down then the buyer of the call option loses money
  3. The money the buyer of the call option would lose is equivalent to the premium (agreement fees) the buyer pays to the seller/writer of the call option
  4. Intrinsic value (IV) of a call option is a non negative number
  5. IV = Max[0, (spot price – strike price)]
  6. The maximum loss the buyer of a call option experiences is to the extent of the premium paid. The loss is experienced as long as the spot price is below the strike price
  7. The call option buyer has the potential to make unlimited profits provided the spot price moves higher than the strike price
  8. Though the call option is supposed to make a profit when the spot price moves above the strike price, the call option buyer first needs to recover the premium he has paid
  9. The point at which the call option buyer completely recovers the premium he has paid is called the breakeven point
  10. The call option buyer truly starts making a profit only beyond the breakeven point (which naturally is above the strike price).

938 comments

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  1. ameheta says:

    Dear sir,
    Can you explain how the premium of call options got diluted while nearing the expiry ? Is there ant formula ?

    • Karthik Rangappa says:

      Time decay besides other factors. We will talk about all of these things eventually in this module. Request you to stay tuned.

      • Prakash says:

        Hi I wanted to know if we buy 8600 PE at 15 ,75 quantity is the minimum required so how much I have to pay to get those shares and what ij case if it goes down to 5 rupees what will be the total loss .. can u pls reply on this as it will be really helpful

        • Karthik Rangappa says:

          You will have to pay 15 * 75 = 1125. If it goes to 5, then the value will be 5*75 = 375 and your loss will be 750.

          • Pradeep says:

            Sir,I bought ACC AUG 1840 CE 1 LOT(400) @ 33 Rps and now would lkie to sell @ 40 today so please help me,what will be my profit and will I lose all my 13200 if I sell today as ACC CMP is 1816 now?

          • Karthik Rangappa says:

            You will make a profit of 7 per unit. Since lot size is 400, your total loss would be 400*7 = 2800

          • Vikash says:

            Hi,

            Just observed 1 point above so the same is posting below:-

            Question by one of the member – Sir,I bought ACC AUG 1840 CE 1 LOT(400) @ 33 Rps and now would lkie to sell @ 40 today so please help me,what will be my profit and will I lose all my 13200 if I sell today as ACC CMP is 1816 now?

            My view – I think he will make profit of 7*400=2800 if sell before expiry.
            Remarks – excluding question regarding ACC CMP 1816.

          • Karthik Rangappa says:

            Yup, he basically makes the difference between the premium he paid and will receive, multiply that with lot size. So 40-33 = 7 and 7*400 = 2800.

          • Ivan says:

            Hi Karthik

            With regards to the earlier query from another member, please could you assist on my query.

            Sir,I bought ACC AUG 1840 CE 1 LOT(400) @ 33 Rps and now would lkie to sell @ 40 today so please help me,what will be my profit and will I lose all my 13200 if I sell today as ACC CMP is 1816 now?

            1. Is is possible for the premium to increase to 40 when the underlying value comes down to 1816?
            2. Should i look out for the increase in premium to consider that i will be in profit or should look out for the underlying value as well?
            3. Wouldn’t the total loss be 13200 as the underlying value is below the strike price?

            Thank you in advance

          • Karthik Rangappa says:

            You bought the option at 33 and selling the same at 40, which means your profit will be Rs.7, multipled by 400 which is 2800. When you sell the option, you will get 40*400 = 16000, which includes the premium and the profit.

            1) Yes, for this to happen the volatility should also increase. This is explained later in the module
            2) If it is a short-term trade, focus on the premium
            3) No.

      • manuski says:

        I knew that CE and PE are to be bought, never sold for huge risk of loss is involved. So forget selling options altogether. If my view is price will go up, I have to buy CE and if my view is price will go down I have buy PE. Be it PE or CE, I have to buy of the strike price which is at the near by value of CMP. Expiry of current month options is always on the last Thursday that month. My questions are ” 1-Can I first buy and then sell PE or CE from last Friday of current to last Thursday of next month at any time in the live market hours?”
        2- ” I bought CE on last Friday of current month. Lot 75. Premium 150. I paid 11250. Mon, Tue, Wed. On Wed Premium is 250 on live chart of my that CE. Can I sell or not? If yes is my profit= 75(250-150)=75*100=7500 ( including brokerage+ charges)?
        3- If I have to day trading of options (only first buy then sell of PE and CE) I need lot size * current premium as capital. For buy today and sell on any day any time before expiry, do I need same capital to buy now? Means lot size * current premium of that option?

        • Karthik Rangappa says:

          1) Yes, you can.

          2) Yes, you can. Yes, you make 100 in profit

          3) Yes, it is the same. No additional margins for buying options. Check this – http://zerodha.com/z-connect/tradezerodha/margin-requirements/zerodha-margin-policies

          • anyket says:

            Dear Sir,
            If i am able to sell my option before expiry then what do you mean when you say ,” Here is an important point to note – you can exercise the option only on the day of the expiry and not anytime before the expiry.”

          • Karthik Rangappa says:

            Exercising an option is only on the day of expiry. However, you can buy and sell the premium at any time frequency.

          • Hits says:

            As you are saying “Exercising an option is only on the day of expiry. However, you can buy and sell the premium at any time frequency”….. that means we may not get profit sometime when even price of the stock increased but its premium price not…before expiry…!!!!

          • Karthik Rangappa says:

            Think of the premium in terms of buying and selling a stock. You make a profit as long as you buy at a lower price and sell at a higher price.

          • Avinash says:

            EX: A Bajaj AUTO option Contract lot of 500 CE strike price 2950 bought on on 15 march at premium 45, expiring on 28 march now premium got increased to 52 and spot price is 2951. If i sell my premium at 52 i will make of 7 rupees on premium and do i have anything to do with spot price at the time of selling my premium and also at the time of expiry date. If spot price increases to 3000 do i incur into any losses.

          • Karthik Rangappa says:

            No, you just have to sell it and pocket the premium of 52. Your profit will be 45-52 = 7.

      • dee says:

        how do i put stop loss i have brought options in normal orderand its in profit but i want to trail stop loss so i dont lose profit in case market turns so how do i put stop loss in this scenario
        2) howdo i put stop loss after i have brought options
        ty

        • Karthik Rangappa says:

          You can do this by placing a regular stop loss and then you can keep modifying the limit price as and when the premium goes higher.

  2. khashu2010 says:

    Hi Karthik, Do we have facility in PI to see payoff charts since it’s required when we play on option strategies (straddle,strangle etc.) ?
    Thanks,
    Ashish

  3. kieron says:

    How to calculate break even point in real market
    Which price take as strike price day starting share price or close price
    And which premium price I take month starting or take everyday different premium prices
    Plz explain it with real market example

    • Karthik Rangappa says:

      Breakeven point is = Strike + Premium paid. It is the same in theoretical and practical world.As I have mentioned in the chapter, selecting the strike price requires some amount of background knowledge on options theory, towards the end of this module you will get a fair understanding on the same.

  4. T RAMA DEVI says:

    Sir, Toaday I bought 8600CE at 75/- Pr. and sold at 85/- with a profit of 10/-per lot. Iam unable to understand, as per formula Break even pt. Strike price + Pr.( 8600+75) indicates nifty should trade above 8675 to be in profit. but I have already got 10/- profit per lot even though nifty not even crossed 8500. Pl. explain. Thanks

    Regards

    • Suren says:

      I too had a same question similar to Rama Devi. Can you please explain ?

      • Karthik Rangappa says:

        Rama / Suren – The break even point is applicable only if you hold the option till expiry. It is not applicable during the series.

    • Yella Reddy Mopuri says:

      Hi rama,
      You said you made a profit of Rs 10 per lot. so here if you have bought one lot what is your total profit ?. Is it 10 rupees or 75*10 = 750 rupees (taking lot size of nifty is 75).

  5. TSS KISHORE says:

    Dear Sir,
    Appreciated for your efforts in teaching for novice traders/investors, I have a doubt; As stated in the above chapter, on 26.03.15 Bajaj Auto 2050CE is at Rs.6.35/- while stock is trading at 2026.90 , today at 3.15pm stock trading at 2025.10 but 2050CE trading at Rs.50/- i.e a profit of Rs. 43.65 per lot. Hence, what is the role of breakeven point, as per rule buyer of 2050 CE option would be in profit only when stock price trades above 2050+6.35= 2056.35. Pl. clarify. Regards

    • TSS KISHORE says:

      Dear Sir, On my above query, I have noted that expiry dates differs, still my question remains same, if we take todays Nifty 8600 CE of April is low 72.50 and at 3.20Pm is Rs. 114.90. If I bought the same CE option when it is at a premium of 80/- and closed at 110/- for a profit of 30/- per lot at the same time Nifty is trading at 8492 Spot. Please clarify.

      • Karthik Rangappa says:

        As I mentioned, during the series, the profitability depends on many other factors. We will get to that as we progress through this module. Request you to stay tuned 🙂

    • Karthik Rangappa says:

      Two things Kishore –

      1) As you have noted it correctly (in your next message) you are looking at two different expiry series. Hence the huge difference.

      2) The break-even point we are discussing in this chapter is ‘Upon Expiry‘. During the series besides the breakeven point there are other important factors that will determine the profitability of the trade. More on these factors when we take up option geeks.

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